Moment of the movement of a mechanical system. What does "the moment of a lot of rush" mean? Higher level of dynamics
- 1. Algebraic the moment of kіlkostі ruhu shchodo center. Algebraic Pro-- scalar value, taken with the sign (+) or (-) and more advanced module of the amount of traffic m on the vіdstan h(perpendicular) from the center to the line, vzdovzh as directions m:
- 2. Vector moment of how much movement there is to the center.
vector the moment of the quantity of movement of the material point about the actual center Pro -- vector, applications at the center and straight lines perpendicular to the vector plane. mі at that bek, the stars of the ruh dots can be seen along the course of the Godinnikov arrow. Tse vznachennya satisfied with vector equanimity
A moment of a lot of rush material points on the same axis z a scalar value is called, taken with a sign (+) or (-) and more module vector projections the amount of movement on the plane, perpendicular to the center of the axis, on the perpendicular h, omissions from the point of the crossbar of the axis with the plane on the line, which is straightened, the projection is shown:
Kinetic moment of the mechanical system to the center of that axis
1. Kinetic moment for the center.
Kinetic moment but the main moment of the number of rushes of the mechanical system of any center called the geometric sum of the moments of the number of movements of all the material points of the system according to that very center.
2. Kinetic moment of any axis.
The kinetic moment is the main moment of the number of points of the movement of the mechanical system, where the axis is, is called the algebraic sum of the moments of the number of points of the movement of all material points of the system, where the axis is.
3. The kinetic moment of a solid body, which wraps around a non-violent z-axis with a windshield.
Theorem about changing the momentum of the number of rotations of a material point along the center of that axis
1. Moment theorem for a center.
Pokhidna for an hour, in view of the moment of the quantity of movement of the material point, such an indestructible center is closer to the moment of force, which is directed to the point, similarly to the center
2. The momentum theorem for any axis.
Pokhidna for an hour, depending on the moment of the quantity of movement of the material point, how long the axis is closer to the moment of force, what is the direction of the point, how the axis is
Theorem about changing the kinetic moment of a mechanical system along the center of that axis
The momentum theorem for a center.
Pokhidna for an hour in the kinetic moment of the mechanical system, something unbreakable for the center is more geometrical sum of the moments in the combined forces, like a system, for the sake of the center;
Consequence. If the head moment of the external forces is equal to zero for some center, then the kinetic moment of the system for any center does not change (the law of conservation of the kinetic moment).
2. The momentum theorem for any axis.
Pokhidna for an hour, in view of the kinetic moment of the mechanical system, it is possible to operate a stable axis
Consequence. If the head moment of external forces is equal to zero, then the kinetic moment of the system does not change along the axis.
For example, = 0, then L z = Const.
Work and the strain of forces
robot force- scalar zahіd dії forces.
1. Elementary robot power.
Elementary of the force robot - an infinitely small scalar value that is equal to the scalar addition of the force vector to the vector of an infinitely small displacement of the force reporting point: ; - increase in radius-vector points of the report of the force, the hodograph of which is the trajectory of the points. Elementary relocation points along the trajectory by virtue of their children. Tom
like that dA > 0;yes, then dA = 0;yes , then dA< 0.
2. Analytical viraz of elementary work.
Imagine a vector і d through their projections on the axes of Cartesian coordinates:
, . Take away (4.40)
3. The work of the force on the end displacement is more integrative sum of elementary work on the total displacement
Like the force has become, and the point of її zastosuvannya moves in a straight line,
4. Robot force of gravity. Vikoristovuemo formula: Fx = Fy = 0; Fz=-G=-mg;
de h- moving the point of stagnation of force vertically down (height).
When the point is moved, the gravity force is uphill A 12 = -mgh(speck M 1 -- at the bottom, M 2 - up).
Otzhe, . The robot of the force of gravity lies in the form of a trajectory. With Russia a closed trajectory ( M 2 M 1 ) work is equal to zero.
5. Robotic spring force.
The spring expands less than the axle X:
F y = F z = O, F x = = -Сх;
de - the value of the deformation of the spring.
When moving the point of the report of the force from the lower position at the top in a straight line, the force of that straight line is shifted, then
To that robot force of springiness
The work of forces at the end of the movement; Yakscho = const, then
de - Kіntseviy ku turn; , de P - number of wraps tila dovkola osi.
Kinetic energy of a material point and a mechanical system. Koenig's theorem
Kinetic energy- scalar entry of mechanical movement.
Kinetic energy of a material point - scalar positive value, which is equal to half of the additional mass of points per square
Kinetic energy of a mechanical system the arithmetic sum of the kinetic energies of the materials used in the system:
The kinetic energy of the system that is accumulated P connected with each other, which is more expensive arithmetic sum of kinetic energies of the system:
Koenig's theorem
Kinetic energy of a mechanical system in the wild trend of the її rush more kinetic energy of the system at once from the center of the mass of the kinetic energy of the system at її rusі to the center of the mass:
de Vkc- speed k- th points of the system to the center wt.
Kinetic energy of a solid body at different temperatures
Progressive Rukh.
The body wrap around the indestructible axis . , de - the moment of inertia of the body is about the axis of wrapping.
3. Plane-parallel ruh. de - the moment of inertia of the flat figure about the axis to pass through the center of the wt.
With flat Russia the body's kinetic energy is formed from the kinetic energy of the progressive movement of the body from the movement of the center of the mass that kinetic energy of the wraparound movement is about the axis, which should pass through the center of mass, ;
Theorem about changing the kinetic energy of a material point
Theorem in differential form.
Differential in the form of kinetic energy of the material point of the healthy elementary robotic force, which is applied to the point,
The theorem in the integral (kintz) form.
Zmina The kinetic energy of the material point on the other moving robotic forces that move on the point are moved on the same.
Theorem about changing the kinetic energy of a mechanical system
Theorem in differential form.
Differential in the kinetic energy of the mechanical system, the sum of the elementary work of the external and internal forces that act on the system.
The theorem in the integral (kintz) form.
Zmina The kinetic energy of a mechanical system is on the basis of a moving moving sum of external and internal forces applied to the system, on the same moving. ; For a system of solids tіl = 0 (for the quality of internal forces). Todi
The law of conservation of mechanical energy of a material point and a mechanical system
Like on the material the point of the mechanical system is no longer conservative force, then whether the position of the point of the system of the sum of kinetic and potential energy is filled with the magnitude of the constant.
For a material point
For mechanical system T+ P= const
de T+ P -- povna mechanical energy of the system.
Solid Body Dynamics
Differential alignment of solid body movement
The number of equalities can be taken from the fundamental theorems of the dynamics of a mechanical system.
1. Equivalence of the translational movement of the body - from the theorem about the movement to the center of the mass mechanical system In projections on the axes of Cartesian coordinates
2. Equal wrapping of a solid body on a slightly indestructible axis - from the theorem about changing the kinetic moment of a mechanical system like an axis, for example, about an axis
Oskilki kinetic moment L z solid body
So, either way, then the level can be written down at the sight, or the form of the record of the level can be deposited depending on what should be taken into account in a specific task.
Differential alignment of plane-parallel ruhi solid body є suupnistyu equal progressive ruhu flat figures together with the center of the mass i overt ruhi shodo osі, scho to pass through the center of the mass:
Physical pendulum
physical pendulum it is called a solid body that wraps around a horizontal axis, that does not pass through the center of the mass of the body, and collapses under the force of gravity.
Differential equal wrapping
The times have small wagons.
Todi, de
Virishennya tsgo homogenous rіvnyannia.
Come on at t=0 Todi
-- equalization of harmonic chimes.
Pendulum swing period
Dozhina of a physical pendulum is the foundation of such a mathematical pendulum, the period of chiselling of some old ancient period of chiselling of a physical pendulum.
Some tasks have a dynamic characteristic of a point that is collapsing, instead of the very small hand, one can look at the same moment, whether it be the center or the axis. Qi moments vynachayutsya as i moments of force.
Moment of a lot of rush material point like a center
The moment of how many times the point is called the same kinetic moment .
Moment of a lot of rush Whatever the axis to pass through the center of the Pro, the better projections of the vector of the number of moves on the whole.
Since the amount of movement is given by its projections on the coordinate axis and the coordinates of the point in space are given, then the moment of the amount of movement for the cob of coordinates is calculated as follows:
Projections to the moment of the volume of movement on the coordinate axes are adjusted:
Alone, vimiryuvannya kіlkostі ruhu on СІ є -.
The theorem about changing the momentum of the number of rotations of a point.
Theorem. Pokhіdna after the hour in view of the moment of the quantity of the movement of the point, taken as the center, the moment of dignity to the point of strength as the same center.
Proof: Differentiate the moment of the amount of movement by the hour
, 
, otzhe, (*)
what it was necessary to bring.
Theorem. Pohіdna after the hour in view of the moment of the quantity of the turn of the point, taken as it were, the axis, the moment of dignity to the point of strength, at the same time, of the axis.
For confirmation, it is enough to design a vector alignment (*) for a whole qiu. For the axis, we look like this:
Lessons from the theorems:
1. If the moment of force when the point reaches zero, then the moment of the momentum when the point is equal to the value has become.
2. If the moment of force, if the axis is equal to zero, then the moment of the force, if the axis is equal, the value has become.
The work of forces. Tension.
One of the main characteristics of strength, which evaluates the force exerted on the body during movement.
Elementary robot power the scalar value is equal to the increase of the elementary displacement onto the projection of the strong displacement.
Alone in the world of robots at SI є -
When at 
Private vipadki:
Elementary displacement to the differential of the radius vector of the force reporting point.
Elementary robot power to the scalar addition of force on the elementary displacement or the differential of the radius of the vector of the point of the report of the force.
Elementary robot power to the scalar addition of the elementary impulse to the strength of the point's mobility.
If the force is set by its projections () on the coordinate axes and elementary displacement is set by its projections () on the coordinate axes, then the elementary work of the force is more expensive:
(Analytical expression of elementary work).
The robot of the force, whether it be the last moving one, is dearer to the taken vzdovzh tsego moving integral in the form of elementary robotics.
Force push the value is called, which is assigned to the robot, which is created by force in one hour. The feeling of exhaustion is more expensive than the first time after an hour in the workplace.
, 
Tension dovnyuє scalar dobutku forces on swidkіst.
Alone vimiryuvannya tightness CІ є -
Techniques take strength for the loneliness 
.
Butt 1. Robot force of gravity.
Let point M, yaku do gravity P, move from position 
at the station. We choose the axis of coordinates so that the entire bula is straightened vertically uphill.
Todi, , , i
The work of the force of gravity is greater than the sign taken with a plus or minus additional force module on the vertical displacement of the point її zastosuvannya. The work is positive, as if the cob point is higher than the end point, and it is negative, so the point is lower than the end point.
Butt 2. Robot force spring.
Let’s look at the material point fixed on the spring element of hardness, as if it’s a chiselling of the axis. The strength of springiness (or the strength that inspires). Let point M, as if there is less spring force, it moves from position to position. ( , ).
The tension of the parity of forces is stronger
Kinetic energy of a point
Kinetic energy material points (or її manpower) call half the dobutku masi specks per square її shvidkostі.
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Catering 1
Under a physical pendulum, one can understand whether it is a body, as if it were small, how to move a non-violent horizontal axis under the force of gravity.
As the last path to designate the position of the center of gravity of the body folding form schodo osі (v_dstan os), looked at the section "Static". For the time period of coliving of the body, it is possible to designate the moment of inertia for the axis Oz, which passes through the point O,
that schodo horizontal axis, scho to pass through the center of the mass of the body.
Tsіkavo sche th such. At the physical bodies, which are pierced, on the extended lines, which pass through the entire wrapping and the center of gravity of the body, the main point is called the center of the chitan.
If the body feels like it’s swaying like the axis, which passes through the center of the splintering, then the period of the splintering of the body will be the same, as if it were splintering, it’s possible for the axis to pass through the point O.
The center of the colivan (point D the little one) is located on the extended line of the OS, lower than the center of gravity of the body with the wind, as it is customary to call the induced dove of the physical pendulum.
Damo to whom I understand such a deed.
Under the induced dozhina of the physical pendulum, the dozhina of the mathematical
The pendulum, the period of coliving of such a long period of coliving of the physical pendulum.
It is easy to point out the point of the pendulum, having equalized the virazi, from which
cyclical frequency of colivans in skin disorders is indicated.
Food 2
Kinetic moment of the point of the system along the center of that axis
Let's look at the system of material points with masses m 1 m 2 ....m n v 1 v 2 .....v n schodo іnertsiynoї system vіdlіku. Viberemo prevіlny center Pro (Fig.1). Kinetic moment points m j to the center is called the vector to the moment її kіlkosti ruhu to the center.
K oj = m o (q j) = r j mj vj(j=1,2...n) (1)
Apparently, the vector multiplier can be written through the attached matrix of the first multiplier-radius of the vector r.
Omitting the index j, we write the matrix virase in the xyz axes with the cob O:
K o=m Rv(2)
de R- skew-symmetric r
= m =m (3)
The projection of the kinetic moment on the whole is called kinetic moment of the point along the axis . Він is calculated either analytically according to formulas (3) or as a moment of force like a axis. The moment is more or less dotichna warehouse vector q(Fig.2).
K Z = + q t h (4)
The moment turns to zero, so that the vector of a lot of movement (the speed of a point) lies in the same plane from the top (it is parallel or it changes the top)
Kinetic moment of the system to the center About the head moment of the number of breaks is called the point of the system to the center.
K o =SK oj =S mj r j v j(5)
Similarly to the formula (3), the projections of the vector (4) satisfy the set of kinetic moments along the coordinate axes
=
Sm j 
(6)
The kinetic moment of the mechanical system of any pole (axis) is called the vector (algebraic) sum of the moments of the number of rotation of all points of the system of any pole Pro(thієї w axis)
(
) . (3.22)
The kinetic moment of a mechanical system is often called the main moment of the system's rotational momentum, similarly to the poles of the axis.
To project the kinetic moment (3.22) on the rectangular Cartesian coordinate axes, then we take the projection of the kinetic moment on the axis or the kinetic moment along the coordinate axes
As the system of material points is collapsing progressively, those, too, .
We hurried to power in the pursuit of happiness vector creative how to use a scalar multiplier and a formula for assigning a radius - a vector to the center mas (2.4).
In this way, the kinetic moment of the pole system in progressive Russia is more equal to the moment of the amount of movement of the system of the wide pole for the mind, that the amount of movement of the system is applied in the center of the mass.
^ Kinetic moment of a rigid body
Rice. eighteen
Let a firm body wrap around in a nearly unbreakable axis with a windshield (Fig. 18). We choose a sufficient point near the solid body and calculate the kinetic moment of this body along the axis of wrapping. Depending on the kinetic moment of the system, it is possible to
.
Ale with wrapping body on the axis,
moreover, the number of points of rotation is perpendicular to the vіdrіzka and located in the plane perpendicular to the axis of the wrap. Otzhe, the moment of how much movement is necessary for the axis for the point
For the whole body 
,
tobto. (3.24)
The moment of inertia of the wrapping body is similar to the wrapping axis until the top of the wrapping body is extended to the same moment of inertia as the wrapping axis.
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Catering 1
According to the principle of possible displacements (basic leveling of statics), in order for a mechanical system to be laid on ideal, stationary, emphasizing and holonomic links, it was in equal position, it is necessary and sufficient, so that all systems had zero:
de Qj- zagalnena force, scho vіdpovidaє j- oh zagalnennoy coordinates;
s- The number of specified coordinates in the mechanical system.
As far as the system was completed, the differential alignment was folded on the form of the Lagrange II alignments - the city, then the designation of the possible positions of the alignment could be adjusted to equalize the cornering force to zero and vice versa to remove the alignment of the cornered coordinates.
If a mechanical system is equal in a potential force field, then equal (1) must be so smart:
Also, the position of equal potential energy can be extremely significant. Not every equal, which is defined by visceral formulas, can be implemented practically. It is important to talk about the stability and inconsistency of this position in the fallow of the behavior of the system when the situation is different.
equal to the mechanical system, the mill of a mechanical system, which perebuvaє under a surge of forces, in which її specks rest a hundred and fifty analyzed reference systems. If the system is considered inertia (div. Inertia system is observed), equal is called absolute, otherwise it is viable. Vivchennya minds R. m. s. - one of the main tasks of statics. Wash R. m. s. to look at the equalities that they tie fiery forces those parameters that determine the position of the system; the number of these minds is equal to the number of steps of the freedom of the system. R. m. s. fold so by itself, as if you had an absolute zeal, as if you were pushing on the points of forces to add more portable forces of inertia. Wash the equalities of a large solid body to rebuy the equalities of zero sums of projections on three coordinate axes Oxyz and the sum of the moments of all the axes of all the forces applied to the body, tobto.
When vikonannі minds (1) tіlo bude, according to the date to this system, it would be necessary to rest at a calm, as if the speed of all yogo points of the balance of the system at the moment the cob of force was equal to zero. In a different way, it was body with a vikonnі of minds (1) Rukh for inertia, for example, collapse progressively, evenly and straightforwardly. If it’s harder the body is not strong (div. mechanical links), then learn to give those equalities (1) (or їx naslіdkіv), so as not to avenge the reactions of overlapping links; Іnshі rіvnostі give rіvnyannya vyznachennya nіdomih reactions. For example, for the body, what can the whole wrapping be indestructible Oz, I will be intellectually jealous mz(F k) = 0; Other equalities (1) serve to determine the reaction of the bearings, which solidify everything. As if the body is fastened with overlays of ties, all equals (1) give a tie for the singing reaction of the ties. Such tasks are often violated in technical terms.
On the basis of the solidification of the principle of equality (1), so as not to avenge the reactions of outrageous links, to give at once the necessary (albeit insufficient) mind, whether it be a mechanical system, zokrema, body, to be deformed. Necessary enough mind Rivnovagi be-like a mechanical system can be known for the help of the possible displacement of the principle. For a system that can s in the steps of freedom, the minds of the mind perebuvayut at the equanimity to zero all the aggravated forces:
Q1= 0, Q2= 0, ×××, Qs= 0. (2)
Zі stanіv rivnovagi, scho vyznachayutsya minds (1) і (2), are practically implemented only tі, yakі є stіyky (div. Stіykіst rivnovagi). The rivers and gases are seen in hydrostatics and aerostatics.
Food 2
Ticket 18
for a vrіvnovazhenoї system of forces, it is already obvious to the principle of the possible displacement of the sum of virtual robotic forces on any possible displacement of the system is guilty of zero.
You can write it down in this way.
At any moment of the collapse of a mechanical system with ideal links, the sum of virtual robots of active forces and forces of inertia on any possible moving system is equal to zero.
Qiu jealousy is accepted to be called
wild jealous dynamics or the Lagrange-D'Alembert principle.
Food 2
"Principle of possible displacement".
This principle is respected by the most implicit mental equivalence of the equal movement of any mechanical system. From this it is possible to take into account all analytical minds and equal bodies under the system of forces, which are seen at the section of "Static".
The principle is formulated as follows:
For a smooth mechanical system with ideal links, it is necessary and sufficient,
so the sum of elementary work of active forces on any possible moving system
valued zero.
In order to prove the necessity of the system, mind the equal, whether it be a mechanical system, which is resting in peace, we divide the forces, which should be the point of the system, on the task and the force of the reaction of the sounds.
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Catering 1
The theory of the gyroscope is approached
A body is called a gyroscope, which makes an unbreakable point and wraps around the axis of material symmetry.
Let's assume that the gyroscope wraps around its axis of symmetry. Whose mind has a kinetic moment
This is one of the most important characteristics of a Russian gyroscope.
In the approximations of the gyroscope theory, it is assumed that 1<< и кинетический момент гироскопа равен
Gyroscope with three steps of freedom
A gyroscope from a trioma with steps of freedom building repair the opir try to change the axis of the wrapping of the gyroscope.
Let's look at the gyroscope, for some kind of neruhom, the point zbіgaєtsya from the center of the mass.
Let's look at the back of the gyroscope (= 0, L= 0). If you apply force to the gyroscope, then it is obvious that the gyroscope will take off the wraparound rotation and fall (so that the entire gyroscope will turn in the plane of the armchair).
Let's look at the gyroscope, what wraps around (shvidko). We apply force.
Behind the theorem about changing the kinetic moment
The moment of perpendiculars to the plane of the armchair, todi
If a force is applied to the axis of the gyroscope, then the entire gyroscope is shifted perpendicularly by the force of the direct torque.
As if the force is attached, the entire wrapping of the gyroscope is ringing. ^ It seems that the gyroscope of the building is the opposite of divine forces.
Let's look at the patterns of regular precession.
Є gyroscope, in which the center of the vag does not break with an indestructible point.
On the body diє strength
Permissible OC = h also
Significantly:
Under the force of gravity, the entire gyroscope wraps around the vertical axis. z. Such a manifestation is called a regular procession.
We introduce the top speed 1 - the top speed, with which the entire gyroscope wraps around the axis z, її still called "kutova shvidkіst pretsії".
Rukh yuli is a good butt of the gyroscope's Rukh.
A gyroscope from three steps of freedom to know more widely in modern systems of orientation (gyrocompass, gyrohorizont ...).
INTERNATIONAL COORDINATIONS
independent parameters qi (i=1, 2, ..., s) be-like space, the number of which took more than the number s of the degree of freedom of the mechanical. systems and yaki unambiguously signify the position of the system. The law of the ruhu system in O. do. given by s levels to the form qi = qi (t), de t - hour. O. to. koristuyutsya with solving many. zavdan, especially if the system is sub-ordered to ties, which imposes an obezhennya її Rukh. For this, the number of equations significantly changes, which describe the dynamics of the system, equal, for example, with the equations in Cartesian coordinates (div. LAGRANGE RIVNYANNYA U MECHANIKU). In systems with an infinitely large number of degrees of freedom (successive medium, physical fields) O. to. є special functions of space coordinates and hour, sound. potentials, hell. functions too.
At the mechanics, the degree of freedom is the combination of independent coordinates of displacement and / or wrapping, which in turn determines the position of the system or the body (and at the same time, following them by the hour - with the help of mill mechanical system or body - that is their camp and ruh).
The number of steps of freedom is the number of independent movements, when the system changes!
in such a manner, with a savage force, which shows the i-th nodal coordinate, the value is called, which is the most important coefficient with the variation of the given nodular coordinate in the pronounced possible work of forces, which can be applied to a mechanical system.
At the peak, the force is fixed - the function of the bounded coordinates, the speed of the points of the system and the hour. It follows that the specified force is a scalar quantity, as to lie in the required for a given mechanical system of specified coordinates. Tse means that when changing the set of cornered coordinates, the initial setting of this system, change and cornering forces. So, for a disk with a radius of r and a mass of m, which rolls without forging on a frail plane (Fig. 18.8), for the narrowed coordinates one can take either s - the coordinate to the center of the mass of the disk, or "fi" - the turn of the disk.
4.1. The power of the system with one step of freedom is recognized
For a system with one degree of freedom, bounded by force, which gives the bounded coordinates q name the value that is defined by the formula
de q- Smaller zbіlshennya zagalnennoї coordinates; - The sum of the elementary forces of the system for the most possible displacement.
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Catering 1
Equation of a two-stage gyroscope.
The level of the two-stage gyroscope is automatically removed from the previous level of the three-stage gyroscope.
signifies the performance of a two-stage gyroscope. Another equal description of the body, on which a two-stage gyroscope is installed.
If the (moment of inertia) of the body is great, and the gyroscopic moment is small, then equal (2) can flare up and become less (1).
Gyroscopic moment:
θ - cut nutation
ω 1 - kutova dryness of wet wrap
ω 2 - speed of precession
J z – moment of inertia
Nutacia - weakly irregular movement of a solid body, which wraps around, which causes precession.
Precession is a phenomenon, for which there is a whole object that wraps around, turns, for example, under the influence of wonderful moments.
It's easy to finish the precession. It is enough to start the jig and bud, until the wine is more calm. On the back, the entire wrapping of the jig is vertical. Then, the upper point gradually descends and collapses in a spiral, to disperse. Tse and є precession of the axis of the jigs.
Zhukovsky's rule: As if the gyroscope is stimulated by the vibrations of the precessionary movement, the gyroscopic couple of forces are responsible, which work the entire gyroscope parallel to the axis of symmetry, moreover, so that the direct wrappings become the same after their turn.
Food 2
As a holonomic mechanical system, it is described by the Lagrangian (- narrowed coordinates, t- hour, the dot indicates differentiation by hour) and in the system there is less potential power, then Lagrange’s equal may look different
de i = 1, 2, … n (n- The number of steps of freedom of the mechanical system). The Lagrangian is the difference between the kinetic and potential energy systems.
As in the system, there are non-potential forces (for example, rubbing forces), Lagrange’s peers may look different
de - the kinetic energy of the system, - the power is aggravated.
Paired with levels in Cartesian coordinates (div., for example, Lagrange's equation of the 1st kind) ur-niya (3) may have that important advantage, that the number of them is equal to the number of steps of freedom of the system and do not lie in the air ) enter to the system of material particles abo til; In addition, with ideal connections from equations (3), all previously unknown reactions of connections are automatically turned off. L. v. The 2nd kind, in order to give even more ardent and before that, to complete the simple method of cherry-picking, they are widely rooted in the wind-up dec. mechanical systems, zokrema in the dynamics of mechanisms and machines, in theory gyroscope, Theoretically, colivan ta in.
Ticket 22
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Theorem about changing the momentum of the number of motion of a material point
Moment of a lot of rush
Moment of how much movement of point M is about the center About the vector, straightening perpendicular to the plane, which should pass through the vector of the number of moves and the center.
Moment of the number of rotations of the point M chodo os and more advanced projection of the vector of the number of ruhu on the plane perpendicular to the axis on the shoulder of the projection along the point of the crossbar of the axis with the plane.
Theorem about changing the momentum of the number of revolutions of the material point to the center
Pokhіdna after the hour in view of the moment of the quantity of movement of the material point, such as a non-violent center, a more geometrical sum of moments of forces that blow on a point, likewise for the center.
The theorem about changing the moment of the quantity of the turn of the material point about the axis
Pohіdna after an hour in the moment of the amount of movement of a material point is perceptible to a non-destructive axis of the sum of the algebra of moments of forces that blow on a point, like a axis.
Law save the moment of the quantity of the flow of the material point
- If the line of diligence applied to the material point of forces constantly passes through some unruly center, then the moment of how much movement of the material point becomes permanent.
- Just as the moment of equal application to the material point of forces, if the current axis is zero for the whole hour, then the moment of the movement of the material point, if the axis is permanent.
Theorem about changing the head momentum of the system's speed
Kinetic moment
The kinetic moment and the main moment of the kіlkostі ruhu of the mechanical system to the center name the vector, the equal geometric sum of the moments in the quantity of the movement of all material points of the system suitable for the center.
The kinetic moment and the head moment of the quantity of movement of the mechanical system name the algebraic sum of the moments of the number of rotations of all material points along the axis
Projection of the kinetic moment of the mechanical system to the center About everything that passes through the whole center, to the kinetic moment of the system to the center of the axis.
The theorem about changing the head momentum of the number of motion of the system (how to the center) - the momentum theorem
Pokhіdna after the hour in view of the kinetic moment of the mechanical system, which is somehow unshakable to the center, is geometrically equal to the head moment of the external forces, which blows on the system, likewise to the center
The theorem about changing the kinetic moment of a mechanical system (how about the axis)
Pohіdna after the hour due to the kinetic moment of the mechanical system, however active axis, is equal to the head moment of external forces, however, the axis.
Law of conservation of the kinetic moment of a mechanical system
- Just as the head moment of the outer forces of something that is indestructible to the center is permanently equal to zero, then the kinetic moment of the mechanical system of the center is constant.
- If the head moment of external forces is equal to zero, then the kinetic moment of the mechanical system is constant.
- The theorem of the moment in May is of great importance for the wrapping movement of bodies and allows you not to guard your own unknown internal forces.
- The internal forces are irresistible to change the main moment of the system's volatility.
Kinetic moment of the overt system
For a system that wraps around a slightly non-violent axis (or an axis that passes through the center of the mass), the kinetic moment of the axis wraps up to the moment of inertia around the axis and the apex of movement.
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Language: Russian, Ukrainian
Butt of a rozrahunka of a spur gear of a cylindrical gear
Butt of a rozrahunka of a spur-toothed cylindrical gear. Vykonaniy vybіr materialu, rozrahunok naprug, scho allowed, rozrahunok on contact and genial mіtsnіst.
Butt rozv'yazannya tasks on the twist beams
At the butt, there was a plot of transverse forces and fundamental moments, an unsafe cut was found and a double tee was picked up. At the task, the following diagrams were analyzed for additional differential fallows;
Butt rozvyazannya tasks on the twisting shaft
The task is to change the steel shaft in terms of the specified diameter, materials and stresses, which are allowed. In the course of the decision, there will be a diagram of moments, what to twist, dotichnyh naprug and twisting. Vlasna vaga val is not insured
Butt of rozvyazannya tasks on raztyaguvannya-squeezing shear
The head of the department is responsible for the revision of the steel shearing strength at the specified voltages, which are allowed. In the course of the decision, there will be a diagram of the later forces, normal stresses and displacement. Vlasna haircut is not safe
Conclusion of the theorem about the conservation of kinetic energy
An example of a perfection of the formulation of the theorem on the conservation of kinetic energy of a mechanical system
Determining speed and speeding up the point for the tasks equal to the pace
The butt of solving tasks on the assignment of speed and speeding up points for tasks equal to the pace
Destination of sharpness and speedy point of a solid body with plane-parallel rus
The butt of the development of tasks on the designation of speeds and speeding up the point of a solid body with plane-parallel Russia
Designated zusil in shears of flat fermi
An example of solving problems on the appointment of zusil in flat fermi shears by the Ritter method and by the method of node observation
Moment of a lot of rush moment
(kinetic moment, moment of impulse, culminating moment), the world of mechanical movement of the body chi system ti l shodo to the center (point) of the axis. To calculate the momentum K material points (tila) the formulas themselves are valid, like the calculation of the moment of force, so replace the vector of force with the vector of the amount of movement mv, then. K = [r· mv], de r- Walk up to the axis wrap. The sum of the momentum in the quantity of motion of all points of the system towards the center (axis) is called the head moment of the quantity of motion of the system (kinetic moment) towards the center (axis). In case of wrapping russ of a solid body, the main moment is the amount of movement z Iz on the apex swidkіst ω tіla, tobto. Kz = Izω.
THE MOMENT OF THE ROCKTHE MOMENT OF THE KILKOSTI RUKHU (kinetic moment, the moment of the impulse, the culminating moment), the world of the mechanical movement of the body or the system of the body, whether it be the center (point) or the axis. To calculate the momentum Before material points (body) the formulas themselves are valid, as is the calculation of the moment of force (div. MOMENT FORCE) so replace the vector of force in them with the vector of the amount of movement mv, zokrema K 0 = [r· mv]. The sum of the momentum in the quantity of motion of all points of the system towards the center (axis) is called the head moment of the quantity of motion of the system (kinetic moment) towards the center (axis). In case of wrapping russ of a solid body, the main moment is the amount of movement z the body is manifested by the additional moment of inertia (div. MOMENT OF INERCE) I z on the top shvidkіst w tіla, tobto. Before Z= I zw.
Encyclopedic dictionary. 2009 .
Marvel at such a "moment of a lot of rush" in other dictionaries:
- (Kinetic moment, culminating moment), one of the entrances of the mechanical the fluctuation of the material point of the system. The role of M. before is especially important. g. rush. Yak і for the moment of force, razrіznyayut M. to. d. to the center (points) i ... Physical Encyclopedia
- (kinetic moment Moment to the impulse, kutovy Moment), the world of the mechanical movement of the body chi system ti l shodo to the center (point) of the axis. For the calculation of the moment, the amount of movement To the material point (tila), the fair itself ... Great Encyclopedic Dictionary
Moment of impulse (kinetic moment, tip moment, orbital moment, moment of momentum) characterizes the quantity of overturnal momentum. The value, yak to lie down, depending on how much the masi wraps around, like it’s rozpodіlena schodo osі.
moment- kinetic moment, one of the entrances of the mechanical movement of a material point or a system. Particularly important is the role of the moment of how much ruhu graє shchodo overt ruhu. Like a moment of strength, a moment is divided ... ... Encyclopedic dictionary of metallurgy
moment- judesio kiekio momentas statusas T sritis Standartizacija ir metrologija apibrėžtis Dydis, lygus dalelės padėties vektoriaus is tam tikro taško y. L = rp; čia L – judesio kiekio momento… …
moment- judesio kiekio momentas statusas t sritis standartizacija ir metrologija apibrėžtis materialiojo taško arba dalelės spindulio vectoriaus ir judesio kiekio vektorinė sandauga. Dažniausiai apibūdina sukamąjį judesį taško arba ašejs, iš kurios yra… Penkiakalbis aiskinamasis metrologijos terminų žodynas
moment- judesio kiekio momentas statusas T sritis fizika atitikmenys: engl. angular moment; moment of momentum; rotation moment vok. Drehimpuls, m; Impulse moment, n; Rotations moment, n rus. momentum, m; moment of momentum, m; cool moment … Fizikos terminų žodynas
Kinetic moment, one of the entrances of the mechanical movement of a material point or a system. The role of M. before is especially important. g. Yak i for the moment of force (...). Great Radianska Encyclopedia
- (Kinetic moment, moment of impulse, tip moment), mechanical world. ruhi tila abo sistem tіl schodo k. l. center (points) or main. For calculation of M. to. e. To the material point (tila), the formulas themselves are valid, which calculate the moment ... Natural science. Encyclopedic dictionary
Those same, scho moment impulsu. Great encyclopedic polytechnic dictionary
Books
- Create, Karl Marx. Another volume of the Works of K. Marx and F. Engels to avenge create, written from spring 1844 to the fierce 1846. For example sickle 1844 p. in Paris, there was a son of Marx and Engels, ...
- Theoretical mechanics. Dynamics of metal structures, V. N. Shinkin. The main theoretical and practical nutrition of the dynamics of the material system and analytical mechanics are examined for such topics: the geometry of mass, the dynamics of the material system of the solid ...
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