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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.
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, except insofar as it is acted upon by ...
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]
The corresponding classical equation of motion is the sinh-Gordon equation. The model can be viewed as a perturbation of Liouville theory. The model's exact S-matrix is known in the weak coupling regime < <, and it is formally invariant under . However, it has been argued that the model itself is not invariant.
The equation for torque is very important in angular mechanics. Torque is rotational force and is determined by a cross product. This makes it a pseudovector. = where is torque, r is radius, and is a cross product. Another variation of this equation is:
Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L .
In Langevin dynamics, the equation of motion using the same notation as above is as follows: [1] [2] [3] ¨ = ˙ + where: . is the mass of the particle. ¨ is the acceleration is the friction constant or tensor, in units of /.
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.