 This article or section is in need of attention from an expert on the subject. WikiProject Physics or the Physics Portal may be able to help recruit one. If a more appropriate WikiProject or portal exists, please adjust this template accordingly. Image File history File links Emblemimportant. ...
 In physics, rigid body dynamics is the study of the motion of a rigid object. Rigid body dynamics differs from particle dynamics in that the body takes up space and can rotate. Image File history File links Broom_icon. ...
A magnet levitating above a hightemperature superconductor demonstrates the Meissner effect. ...
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. ...
In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. ...
Space has been an interest for philosophers and scientists for much of human history. ...
This article is about rotation as a movement of a physical body. ...
Briefly summerised particles have:  no rotation
 linear veloctiy
 mass
Wheras rigid bodies have: Rigid bodies can not be deformed, unlike Soft body dynamics. Most game Physics engines simulate forward rigid body dynamics. Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...
Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg mÂ², Former British units slug ft2), is the rotational analog of mass. ...
Soft body dynamics is an area of physics simulation software that focuses on accurate simulation of a flexible object. ...
A physics engine is a computer program that simulates Newtonian physics models, using variables such as mass, velocity, friction and wind resistance. ...
Note: This article has much overlap with the rigid rotor and rigid body articles. Articles should eventually be merged. The rigid rotor is a mechanical model that is used to explain rotating systems. ...
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. ...
Equations from particle dynamics can be generalized to rigid body dynamics as follows: Rigid body linear momentum
The equation for particle linear momentum is In physics, momentum is a physical quantity related to the velocity and mass of an object. ...
where:  m is the particle's mass.
 v is the particle's velocity.
 f_{i} is one of the N forces acting on the particle.
Assuming constant mass, this reduces to To generalize assume a body of finite mass and size is composed of such particles. There exist internal forces, acting between any two particles, and external forces, acting only on the outside of the mass. Each particle has:  a mass dm.
 a position vector r.
Thus, the linear momentum equation of any given particle would look like this: If the equation for each particle were added together, the internal forces would cancel out, since by Newton's third law, any such force would have opposite magnitudes on the two particles. Also, the left side would become an integral over the entire body, and the second derivative operator could come out of the integral, leaving Letting M be the total mass, the left side can be multiplied and divided by M without changing the validity: However, is the formula for the position of center of mass. Denoting this by r_{cm}, the equation reduces to In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ...
Thus, linear momentum equations can be extended to rigid bodies by denoting that they describe the motion of the center of mass of the body.
Rigid body angular momentum The most general equation for rotation of a rigid body in three dimensions about an arbitrary origin O with axes x, y, z is where: Here is the moment of inertia tensor and is the angular velocity (a vector). Based on this, a theorem states that any rigid body is equivalent when moving to a Poinsot's ellipsoid. Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg mÂ², Former British units slug ft2), is the rotational analog of mass. ...
Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...
Poinsots construction is a geometrical method for visualizing the torquefree motion of a rotating rigid body. ...
Further  ω_{q} is the angular velocity about axis q.
 M is the total mass.
 b_{G/O} is the vector from O to the body's center of mass.
 R_{O} is the position of O.
 t is time.
 is an integral over the mass of the body.
 τ_{O,j} is one of the N moments about O.
This equation follows from equation for linear momentum of a particle and kinematics; no additional observations of nature are necessary to arrive at it. There are many special cases that simplify this equation. The first term goes to zero if any of three conditions are met:  O is a fixed point (since its second derivative would be zero).
 A set of axes is chosen with its origin attached to the body's center of mass (since this would reduce the vector b to zero).
 The vector b always points in the direction of the acceleration of O (since the cross product of parallel vectors is zero).
Also, if the axes are chosen are the principal axes (i.e., the moments about the xy, xz, and yz planes is zero), the offdiagonal terms of the matrix are zero. This case is further discussed by Euler's equations. In physics, Eulers equations govern the rotation of a rigid body. ...
When learning about angular motion, students are generally first exposed to the case of rotation only in the xy plane and a fixed axis or axis at the center of mass with constant rotational inertia. That equation is Angular momentum and torque Similarly, the angular momentum for a system of particles with linear momenta p_{i} and distances r_{i} from the rotation axis is defined This gyroscope remains upright while spinning due to its angular momentum. ...
For a rigid body rotating with angular velocity ω about the rotation axis (a unit vector), the velocity vector may be written as a vector cross product In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length, (or magnitude) is 1. ...
In mathematics, the cross product is a binary operation on vectors in three dimensions. ...
where  angular velocity vector
 is the shortest vector from the rotation axis to the point mass.
Substituting the formula for into the definition of yields where we have introduced the special case that the position vectors of all particles are perpendicular to the rotation axis (e.g., a flywheel): . Spoked flywheel Flywheel from stationary engine. ...
The torque is defined as the rate of change of the angular momentum Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ...
If I is constant (because the inertia tensor is the identity, because we work in the intrinsecal frame, or because the torque is driving the rotation around the same axis so that I is not changing) then we may write where  α is called the angular acceleration (or rotational acceleration) about the rotation axis .
Notice that if I is not constant in the external reference frame (ie. the three main axes of the body are different) then we cannot take the I outside the derivate. In this cases we can have torquefree precession. Precession of a gyroscope Precession refers to a change in the direction of the axis of a rotating object. ...
Applications Computer physics engines use rigid body dynamics to increase interactivity and realism in video games. A physics engine is a computer program that simulates Newtonian physics models, using variables such as mass, velocity, friction and wind resistance. ...
This article is about computer and video games. ...
See also Theory Simulators In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. ...
The rigid rotor is a mechanical model that is used to explain rotating systems. ...
Soft body dynamics is an area of physics simulation software that focuses on accurate simulation of a flexible object. ...
A multibody system is used to model the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements. ...
The details of a spinning body may impose restrictions on the motion of its angular velocity vector, Ï‰. The curve produced by the angular velocity vector on the inertia ellipsoid, is known as the polhode, coined from Greek meaning path of the pole. The surface created by the angular velocity vector...
Precession of a gyroscope Precession refers to a change in the direction of the axis of a rotating object. ...
Poinsots construction is a geometrical method for visualizing the torquefree motion of a rotating rigid body. ...
A physics engine is a computer program that simulates Newtonian physics models, using variables such as mass, velocity, friction and wind resistance. ...
The Physics Abstraction Layer (PAL) is an open source cross platform physics engine API abstraction system. ...
RigidChips is a solid body simulator developed by The student. In RigidChips, various objects can be freely produced by combining parts, and setting the script to them. ...
External links  Chris Hecker's Rigid Body Dynamics Information
 Physically Based Modeling: Principles and Practice
 Gyration  Open source software simulating a blockshaped mass floating in free space
 DigitalRune Knowledge Base contains a master thesis and a collection of resources about rigid body dynamics.
 Stability of a rigid body spinning freely in space from Hugh Hunt's Dynamics Movies page
