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There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
In fact, Appell's equation leads directly to Lagrange's equations of motion. [3] Moreover, it can be used to derive Kane's equations, which are particularly suited for describing the motion of complex spacecraft. [4] Appell's formulation is an application of Gauss' principle of least constraint. [5]
Since linear motion is a motion in a single dimension, the distance traveled by an object in particular direction is the same as displacement. [4] The SI unit of displacement is the metre . [ 5 ] [ 6 ] If x 1 {\displaystyle x_{1}} is the initial position of an object and x 2 {\displaystyle x_{2}} is the final position, then mathematically the ...
For continuous bodies these laws are called Euler's laws of motion. [ 7 ] The total body force applied to a continuous body with mass m , mass density ρ , and volume V , is the volume integral integrated over the volume of the body:
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. [3] More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables.
Kepler's equation; Kepler's laws of planetary motion; Kirchhoff's diffraction formula; Klein–Gordon equation; Korteweg–de Vries equation; Landau–Lifshitz–Gilbert equation; Lane–Emden equation; Langevin equation; Levy–Mises equations; Lindblad equation; Lorentz equation; Maxwell's equations; Maxwell's relations; Newton's laws of ...
Einstein field equations; Einstein–Rosen metric; Electromagnetic wave equation; Elliott formula; Emden–Chandrasekhar equation; Ensemble (mathematical physics) Equation of state; Equations of motion; Euler's laws of motion
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]