rigidbody

A rigid body is an ideal object in which the relative positions of all its constituent particles remain fixed in time. This implies no elastic deformation under any forces; distances and angles within the body are invariant. In many problems the rigid body is treated as a solid that can translate and rotate as a whole.

The motion of a rigid body can be described by the position of its center of mass and its orientation. The center of mass position r and velocity v describe translation; the body's orientation is often represented by a rotation matrix, a set of Euler angles, or a quaternion. The angular velocity ω describes the rate of rotation, and the inertia tensor I encodes how mass is distributed relative to the center of mass. In general the angular momentum is L = I · ω, or more explicitly for a non-symmetric body, L = ∑ m_i r_i × v_i.

Equations of motion: translational motion m a = F_ext, where a is the acceleration of the center of mass and F_ext is the total external force. Rotational motion about the center of mass is governed by the torque equation dL/dt = τ_ext. For a fixed-axis rotation, L = I ω reduces to a scalar relation; in the general case the relation uses the inertia tensor, and Euler's equations apply if expressed in the rotating frame.

Conservation: in the absence of external forces, linear momentum and angular momentum are conserved. In practice, rigid-body models neglect deformation and are an approximation; real objects deform under large loads or high speeds, and the tensor I changes with orientation.

Applications: rigid-body dynamics are used in engineering, robotics, spacecraft attitude dynamics, computer graphics, and biomechanics. The concept provides a tractable description of many systems where internal deformations are small or neglected.