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For reference and background, two closely related forms of angular momentum are given. In classical mechanics, the orbital angular momentum of a particle with instantaneous three-dimensional position vector x = (x, y, z) and momentum vector p = (p x, p y, p z), is defined as the axial vector = which has three components, that are systematically given by cyclic permutations of Cartesian ...
Angular momentum is a property of a physical system that is a constant of motion (also referred to as a conserved property, time-independent and well-defined) in two situations: [citation needed] The system experiences a spherically symmetric potential field. The system moves (in quantum mechanical sense) in isotropic space.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
If a system of particles, , =, …,, are assembled into a rigid body, then the momentum of the system can be written in terms of positions relative to a reference point , and absolute velocities : =, = + = +, where is the angular velocity of the system and is the velocity of .
Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net effect. [ 3 ] The linear momentum of a rigid body is the product of the mass of the body and the velocity of its center of mass v cm .
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration). The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2).
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics, [7] kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton.