Dynamics

Dynamics (Greek δύναμις - force) is a section of mechanics that studies the causes of mechanical motion. Dynamics operates with such concepts as mass, force, momentum, momentum, energy.
Dynamics is also often referred to, in relation to other fields of physics (for example, field theory), that part of the theory that is more or less directly analogous to dynamics in Mechanics, as opposed to kinematics (to kinematics in such theories is usually referred to, for example, the ratios obtained from transformations of magnitudes when changing the frame of reference). It is simply a process that evolves over time, depending on the time of some magnitude, not necessarily referring to the specific mechanism or cause of that dependence.
Dynamics based on Newton's laws are called classical dynamics. Classical dynamics describes the movements of objects at speeds from millimeters per second to kilometers per second. However, these methods cease to be valid for the motion of objects of very small size (elementary particles) and for motions at speeds close to the speed of light. Such movements are subject to other laws.
The laws of dynamics also study the motion of a continuous medium, ie, elastically and plastically deformed bodies, liquids, and gases. celestial mechanics, ballistics, ship dynamics, aircraft. hydrodynamics, aerodynamics, etc.
Contents
1 The main task of dynamics
2 Newton's laws
3 Newton's laws in non-inertial reference systems
4 Dynamics description based on the principle of least action
5 Formulas of some forces different nature
6 See. also
7 Notes
8 Literature
9 Force
The main task of dynamics
Historically, the division into the forward and reverse dynamics of a problem is as follows.
The direct task of dynamics: to determine the equilibrium by a given nature of motion The forces acting on the body. The inverse dynamics problem: determine the nature of the motion of the body by given forces.
Newton's Laws
More: Newton's Laws Classical dynamics is based on Newton's three fundamental laws:
1 th: There are reference systems in relation to which the moving body keeps its velocity constant, if but it is not acted upon or compensated by other bodies.
2: In inertial frames of reference, the acceleration received by a material point is directly proportional to the force causing it, coincides with it in the direction, and inversely proportional to the mass of the material point.
where - the acceleration of the body - the forces applied to the material point, and - its mass, or
In classical (Newtonian) mechanics the mass of a material point is considered to be constant over time and independent of any features of its motion or interaction with other bodies [1] [2].
Newton's second law can be taco formulate using the concept of momentum:
In inertial reference systems, the derivative of the momentum of a material point in time is equal to the force acting on it [3]. where where is the momentum (amount of motion) of a point, its velocity, and - time . With this formulation, it is still believed that the mass of a material point is constant over time [4] [5] [6].
3rd: Bodies act one on one with forces equal in modulus and opposite in direction < If at the same time consider the interaction of material points, then both forces act along the line that connects them. This leads to the fact that the total momentum of the system consisting of two material points in the interaction process remains unchanged. Thus, from the second and third laws of Newton, one can obtain the laws of conservation of momentum and momentum.
Newton's laws in non-inertial reference systems
The existence of inertial reference systems is only postulated by Newton's first law. Real-world reference systems, such as the Earth or the Sun, do not have the full property of inertia through circular motion. It is impossible to experimentally prove the existence of an inertial frame of reference, since it requires a free body (bodies that are not affected by any forces), and that the body is free can only be shown in the inertial frame of reference. Description of motion in non-inertial reference systems that move with acceleration relative to inertia requires the introduction of so-called dummy forces, such as inertia force, centripetal force, or Coriolis force. These "forces" are not conditioned by the interaction of bodies, that is, by their nature are not forces and are introduced only to preserve the form of Newton's second law:
, where where is the sum of all the dummy forces that arise in a non-inertial frame of reference. Description of dynamics based on the principle of least action
Many laws of dynamics can be described not based on the laws of Isaac Newton, but from the principle of least action.
Formulas of some forces of different nature
The power of gravity:
or vector form:
near the earth's surface:
Friction force:
Archimedes force:
See. Also Hydrodynamics - Gas Dynamics - Thermodynamics - Aerodynamics - Statics - Notes
↑ Markeyev AP Theoretical Mechanics ..
↑ Targ SM Short Course theoretical mechanics. - ISBN 5-06-003117-9.
↑ Sivukhin DV The general course of physics. - T. I. Mechanics. - ISBN 5-9221-0225-7.
↑ Markeyev AP Theoretical mechanics. “… Newton's second law is valid only for a point of sustainable composition. Dynamics of systems of variable composition requires separate consideration »
↑ Irodov IE Basic laws of mechanics.« In Newtonian mechanics ... m = const and dp / dt = ma ».
↑ Kleppner D., Kolenkow RJ An Introduction to Mechanics. - P. 112. - ISBN 0-07-035048-5. "For a particle in Newtonian mechanics, M is a constant and (d / dt) (Mv) = M (dv / dt) = Ma". Literature
VA Aleshkevich, LG Dedenko , VA Karavaev Solid State Mechanics. Lectures. Publishing House of the Faculty of Physics, MSU, 1997.
Matveev. AN Mechanics and theory of relativity. M .: Higher School, 1986. (3rd ed. M .: ONICS 21st Century: World and Education, 2003. - 432s.)
Pavlenko Yu. G. Lectures on Theoretical Mechanics. M .: FIZMATLIT, 2002. - 392s.
Sivukhin DV The general course of physics. In 5 vols. Volume I. Mechanics. 4th ed. M .: FIZMATLIT; MFTI Publishing House, 2005. - 560 pp. - Yavorsky BM, Detlaf AA Physics for high school students and university students: a textbook. M .: Drofa, 2002, 800s. ISBN 5-7107-5956-3 - M.O. Kilchevskyi, Course of Theoretical Mechanics in Two Volumes, Vol. 2, Dynamics of Systems, Kyiv, Nat. T. Shevchenko, 2009, 447 pp. - Silky


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