CONSTRAINTS

Constraints in a dynamic system are prescriptions on the motion of the system which act to reduce the number of degrees of freedom in the system. In a system with n discrete rigid bodies, there 6n basic degrees of freedom, because each body may translate in three dimensions and and rotate in three dimensions. When constraints are present, the number of degrees of freedom is reduced by the number of constraints.

Physically, constraints may be imposed by attachments outside the system which restrict motion of one or more bodies in the system. Physical constraints vary greatly in their form and effect on the system dynamics. Numerous examples are listed in the Examples and Applications sections.

Mathematically, constraints are represented as algebraic relationships among the variables in the system. The constraint relations may be as simple as a specification that there is no motion in a particular direction, or they may be much more complicated. In developing equations of motion for the dynamic system, the algebraic relations prescribed by the constraints allow algebraic substitutions to be made in the equations to eliminate one or more variables. Each constraint present in the system reduces the number of degrees of freedom by one and also makes it possible to remove one variable from the equations of motion. After applying all system constraints, the remaining variables in the system are referred to as the generalized coordinates.