In the Newtonian Dynamics of the multibody mechanical systems (MBS), the most general theorem is considered the kinetic energy theorem in the differential form. In the advanced studies on the MBS have led to existence of some higher energy, corresponding to accelerations of higher order. According to the literature the general principles underlying the entire analytical dynamics are: the principle of D`Alembert, the principle of virtual mechanic work, specific to dynamic behavior of mechanical systems, known as D’Alembert-Lagrange principle. The second part of the paper is focused on a few formulations, based on author research on advanced dynamics of multibody systems, when they are characterized by sudden and transitory motions. It demonstrates theoretical and experimental the existing of time variations in accelerations. According to main author research, they are integrated into higher order energies and these in the differential equations of motion in higher order, which will lead to variations in time of generalized forces which they are dominating the mechanical systems with sudden and transitory motions.

Key words: analytical dynamics, acceleration energies, differential principles, dynamics equations.

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