Equivalence of Euler equations and torque-angular momentum relation | Zendy

Vedat Tanrıverdi | Zendy

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Equivalence of Euler equations and torque-angular momentum relation

Author(s) -

Vedat Tanrıverdi

Publication year - 2021

Publication title -

revista mexicana de física e

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.178

H-Index - 10

eISSN - 2683-2216

pISSN - 1870-3542

DOI - 10.31349/revmexfise.18.136

Subject(s) - angular momentum , classical mechanics , reference frame , rotating reference frame , torque , moment of inertia , mathematics , rigid body , mathematical analysis , euler's formula , physics , equations of motion , total angular momentum quantum number , euler angles , infinitesimal , frame of reference , euler equations , frame (networking) , geometry , quantum mechanics , telecommunications , computer science

Euler derived equations for rigid body rotations in the body reference frame and the stationary reference frame by considering an infinitesimal part of the rigid body. Another derivation is possible, and it is widely used: transforming torque-angular momentum relation to the body reference frame. However, their equivalence is not shown explicitly. In this work, for a rigid body with different moments of inertia, we calculated Euler equations explicitly in the body reference frame and the stationary reference frame and torque-angular momentum relation. We also calculated equations of motion from Lagrangian. These calculations show that all four of them are equivalent.

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