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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.
This formulation yields one equation because there is a single parameter and no constraint equation. This shows that the parameter θ is a generalized coordinate that can be used in the same way as the Cartesian coordinates x and y to analyze the pendulum.
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 the inertial frame, the differential equation is not always helpful in solving for the motion of a general rotating rigid body, as both I in and ω can change during the motion. One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant.
The original Langevin equation [1] [2] describes Brownian motion, the apparently random movement of a particle in a fluid due to collisions with the molecules of the fluid, = + (). Here, v {\displaystyle \mathbf {v} } is the velocity of the particle, λ {\displaystyle \lambda } is its damping coefficient, and m {\displaystyle m} is its mass.
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force.
The right-hand side of this equation is treated as an inertial force. A free motion equation need not exist in general. It can be defined if and only if a configuration bundle Q → R {\displaystyle Q\to \mathbb {R} } of a mechanical system is a toroidal cylinder T m × R k {\displaystyle T^{m}\times \mathbb {R} ^{k}} .
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
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