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Rigid body motion theory is a fundamental and well-established part of physics. It is based on the approximation that for stiff materials, any force applied to a body produces a negligible deformation.

**Rigid and deformable bodies**

Rigid body motion theory is a
fundamental and well-established part of physics. It is based on the
approximation that for stiff materials, any force applied to a body produces a
negligible deformation. Thus, the only change a force can produce is change in
the center of mass motion and change in the rotational motion. This means that
simulation of even complex bodies is relatively simple, and thus this method
has become popular in the computer simulation field.

Given the forces acting on the body, the motion can
be determined using ?? ??for translational motion, and a similar relation for
rotational motion .

The rigid body motion model has traditionally been
applied in range analysis in CAD and for computer animation where deformation
is not required. If the deformation is not negligible, then the approximation
does not hold, and we need to start over and come up with some other model.
There exists many different models, but the two models which have emerged to
become the most widely used in practice are: mass-spring models and statics
models solved using the Finite Element Method (FEM).

Mass-spring models represent bodies as discrete
mass-elements, and the forces between them are transmitted using explicit
springandisnot limited to pure Hooke interactions). Given the forces acting on
an element, we can determine its motion using . The motion of the entire body
is then implicitly described by the motion of its elements.

Mass-spring
models have traditionally been applied mostly for cloth simulation. Statics
models are based on equilibrium relations, and thus make the approximation that
the effect of dynamics are negligible. Relations between the strain and stress
fields of a body are set up, and through specifying known values of these
fields, through for example specifying forces acting on the body, the unknown
parts can be determined. These relations form differential equations, and the
known values are boundary values. The FEM is an effective method for solving
boundary value problems, and has thus given its name to these types of
problems. Statics models have traditionally been applied in stress and
displacement analysis systems in CAD.

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