A special feature of employment of Lagrange’s equations to the scleronomic mechanical systems

The research aims to reduce the volume of mathematical manipulations during a derivation of Lagrange’s equations of scleronomic mechanical systems. Corresponding equations are derived using a direct substitution of the kinetic energy expression as homogenous quadratic function in Lagrange’s equations of a general form. The reduction of mathematical manipulations is obtained avoiding of a member, which appears firstly as positive and secondly as a negative expression. A half of nonzero terms can be omitted using this shape of Lagrange’s equations of the second type. Three examples of scleronomic systems support the idea of the research.