Deriving Euler-Lagrangian equations of motion for sophisticated mechanical systems symbolically often results in complex and large expressions. Based on algorithmic differentiation we present an alternative to the direct implementation of this equations. The Lagrangian provides the starting point for deriving the equations of motion and not necessarily has to be given explicitly. Algorithms containing loops or other control structures will work as well. We will demonstrate the usage of this alternative differentiation method on the system of a tower crane. Experimental results will complete this proposal.