Constructing Dynamic Equations of Constrained Mechanical Systems

In this paper constructing equation of mechanical systems based on their kinetic energy, potential energy and dissipative force is discussed. Both the holonomic and non-holonomic constraints are considered. Equations of constraint forces resulting from ideal and non-ideal nature of the constraints are developed.It is shown that, the constraint force is a sum of two forces resulting from the ideal and non-ideal nature of the constraints. An explicit equation of the acceleration of the system is developed basing on the constraint forces from the nature of the constraints. For investigating the deviation of the system from the trajectory of the constraint equations, excess variables are included in the equations of the constraints. The stability of the system is based on determining the sign of constants emerging from developing the Lagrange’s equation of motion for the constraints. The determination of the sign of the constants is made based on Routh-Hurwitz Criterion for Stability. An example is used to demonstrate each of the equations developed in the paper and constructing state-space equation of the system.

dissipative force, excess variables, ideal constraints, Lagrange equation, non-ideal constraints, stability, Routh-Hurwitz criterion for stability, state-space equation