Rigid body dynamics
Under the rigid-body simulation (English Rigid Body Simulation ) is the time- continuous or discrete simulation of the motion of rigid bodies (English Rigid Body ), which represent a physical modeling of spatially extended objects.
The movement of the body is described by ordinary differential equations, to which a solution of an initial value problem must be found in the course of the simulation. The motion consists of translation, rotation and mirroring, which can occur no reflection at a steady equation of motion.
Rigid body
A rigid body consists of a set of particles ( mass points ) have a fixed rigid relationship. The state of a rigid body is defined by:
- Position X (t) ( position of the center of gravity of the rigid body in space)
- Orientation Q ( t) ( usually expressed as a quaternion )
- Total pulse P (t)
- Angular momentum L (t)
Furthermore, a part of the total mass M and the inertia tensor with the immutable properties of the body. During the simulation of the orientation of the body is dependent on the inertia tensor must be calculated. This is done by the following equation:
Wherein the rotation matrix R (t) from the orientation of Q (t) can be calculated.
Rigid Body Motion
The translational and rotational motion of a rigid body is influenced by the following factors:
- Velocity v ( t)
- Rotation speed
- Linear acting forces F (t) ( movement forces which act on the object )
- -acting torque ( rotational forces acting on the object)
As a result, the following general equation of motion are defined:
, Which is valid for.
The solution of the initial value problem of this differential equation has to be solved in the computer simulation by means of numerical methods such as the Runge- Kutta method.
Collision detection and response
Collision detection is to locate part of the rigid body simulation to collisions among rigid bodies and take the appropriate collision responses. Collision responses are usually physical reactions, such as an elastic shock, alter the movement of the rigid body.
Engines
- Computer game development
- Animation
- Computational Physics