This section describes equations of motion.
Consider a mechanical system defined in the following way:
- A set of design variables,
- A set of states,
- A set of constraints,
The set of states,
x, consist of:
- Displacements
- Velocities
- Lagrange Multipliers
- Auxiliary variables such as user-variables and states for user-differential
equations
With this notation, the equations of motion for a mechanical system can be expressed
as:
-
-
The initial conditions for the mechanical system are prescribed as:
(1)
For notational simplicity, henceforth,
will simply be referred to as
. The states,
, are required to satisfy the above equations at all
points in time.