Define the generalized coordinates
Write the constraint equations
Differentiate the constraints with respect to time
Form the velocity constraints
Differentiate again to obtain acceleration constraints
Identify independent and dependent variables
Reduce the system using the constraints
Apply Newton’s laws or Lagrange’s equations
Introduce Lagrange multipliers if constraint forces are needed
Solve the resulting linear system
Check consistency with the original constraints
Compute the motion variables of interest
Verify initial conditions and boundary conditions
Validate the solution against physical limits