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About Using Moment of Momentum and Angular Velocity Vectors for Description of Rotational Motions of a Rigid Body
Author(s) -
Krivtsov A.M.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200106)81:6<393::aid-zamm393>3.0.co;2-y
Subject(s) - angular velocity , rigid body , moment of inertia , angular momentum , scalar (mathematics) , mathematical analysis , moment (physics) , classical mechanics , mathematics , eigenvalues and eigenvectors , euler angles , euler's formula , principal axis theorem , physics , euler equations , tensor (intrinsic definition) , basis (linear algebra) , curl (programming language) , vector field , geometry , computer science , quantum mechanics , programming language
Two sets of vector variables for the analysis of rotational motions of a rigid body are presented. The first set consists of the vector projections of the angular velocity on the eigenvectors of the inertia tensor, the second one is based on the angular velocity and moment of momentum vectors. Vector analogues of the dynamic Euler equations are obtained for the considered variables. The presented equations allow to determine the orientation of the rigid body in space, whereas analysis of the classic Euler equations gives only scalar projections of the angular velocity on the body‐fixed basis. However, the similarity of the proposed vector equations to the classic scalar ones allows application of the similar mathematical methods for the problem analysis. Example problems were solved using the proposed methods.