Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Superposition of Motions in The Space of Lagrange Variables

Version 1 : Received: 11 January 2021 / Approved: 12 January 2021 / Online: 12 January 2021 (15:05:35 CET)

How to cite: ALYUSHIN, Y. Superposition of Motions in The Space of Lagrange Variables. Preprints 2021, 2021010225 (doi: 10.20944/preprints202101.0225.v1). ALYUSHIN, Y. Superposition of Motions in The Space of Lagrange Variables. Preprints 2021, 2021010225 (doi: 10.20944/preprints202101.0225.v1).

Abstract

The technique of superposition of motions in the space of Lagrange variables is described, which allows us to obtain the equations of combined motion by replacing the Lagrange variables of superimposed (external) motion with Euler variables of nested (internal) motion. The components of velocity and acceleration in the combined motion obtained as a result of differentiating the equations of motion in time coincide with the results of vector addition of the velocities and accelerations of the particles involved in the superimposed motions at each moment of time. Examples of motion and superposition descriptions for absolutely solid and deformable bodies with equations for the main kinematic characteristics of motion, including for robot manipulators with three independent drives, pressing with torsion, bending with tension, and cross– helical rolling, are given. For example, given the fragment of calculation of forces in the kinematic pairs shown the advantages of the description of motion in Lagrangian form for the dynamic analysis of lever mechanisms, allows to determine the required external exposure when performing the energy conservation law at any time in any part of the mechanism.

Subject Areas

continuous medium; equations of motion; Lagrange variables; superposition; dynamic analysis

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