  A conventional derivation of motion equations in mechanics and field
equations in field theory is based on the principle of least action with a
proper Lagrangian. With a time-independent Lagrangian, a function of
coordinates and velocities that is called energy is constant. This paper
presents an alternative approach, namely derivation of a general form of
equations of motion that keep the system energy, expressed as a function of
generalized coordinates and corresponding velocities, constant. These are
Lagrange equations with addition of gyroscopic forces. The important fact, that
the energy is defined as the function on the tangent bundle of configuration
manifold, is used explicitly for the derivation. The Lagrangian is derived from
a known energy function. A development of generalized Hamilton and Lagrange
equations without the use of variational principles is proposed. The use of new
technique is applied to derivation of some equations.
