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Application of Moving Frame Method to Solve 3D Dynamics Problems

[+] Author Affiliations
Amir G. Rezaei, Shannon Lee

California State University, Pomona, CA

Thomas J. Impelluso

Bergen University College, Bergen, Norway

Paper No. IMECE2016-68000, pp. V04AT05A032; 10 pages
doi:10.1115/IMECE2016-68000
From:
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4A: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5054-1
  • Copyright © 2016 by ASME

abstract

This paper presents application of a new method to solve 3D Dynamics problems. Briefly: 1. The method uses the special orthogonal group, SO(3), and the special Euclidean group, SE(3), of the Lie Algebra. 2. The method uses Cartan’s Moving Frames 3. The method uses a new notation developed in the discipline of Geometrical Physics.

The method makes 3D Dynamics easier than 2D. It offers a more efficient way to model dynamics of rigid bodies and a new approach to linked mechanisms. The new method is founded on rigorous math and avoids the historical ambiguities that accompany traditional methods (such as the vector cross product that produces pseudo-vectors). It is easily learned with the simple mathematical tools of matrix multiplication and second semester calculus. We plan to apply the method to two different 3D dynamics problems: 1. Holonomic and 2. Non-holonomic. The solutions using the new method will be compared to the traditional method in Dynamics.

Copyright © 2016 by ASME

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