After taking two time derivatives, we can put this into a standard constraint matrix equation form The constraint matrix has pseudoinverse We allow there to be sliding friction between the block and the inclined plane. We parameterize this force by a standard coefficient of friction multiplied by the normal force Whereas the force of gravity is reversible, the force of friction is not. Therefore, the virtual work associated with a virtual displacement will depend on C. We may summarize the three forces (external, ideal constraint, and non-ideal constraint) as follows: Combining the above, we find that the equations of motion are This is like a constant downward acceleration due to gravity with a slight modification. If the block is moving up the inclined plane, then the friction increases the downward acceleration. If the block is moving down the inclined plane, then the friction reduces the downward acceleration. References Dynamics (mechanics) Classical mechanics Theoretical physics Mathematical physics