In this study, different forms of Lagrangian and Hamiltonian based energy functions are represented to analyze an engineering (or a physical) system. Both systems, linear and nonlinear, are analyzed in the same way using the approaches above. Based on tensorial quantities: contravariant generalized coordinates q(i), velocities q(i) and covariant generalized momenta p(i), one can obtain different forms of Lagrangians and Hamiltonians, and so different forms of equations of generalized motion as long as number of the inertial elements is equal to the degree of freedom of a generalized motion. How these forms, namely covariant, contravariant & a mix of a physical system and different forms of equations of generalized motion are achieved is explained. The approach is illustrated through a (trivial) electromechanical example. The question as to which form is better for a given physical (or engineering) system is still open and needs further study.