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On the rotational equations of motion in rigid body dynamics when using Euler parameters
Karim Sherif1, Karin Nachbagauer2, Wolfgang Steiner2
1Johannes Kepler University of Linz, Altenbergerstr. 69, 4040 Linz, Austria.
Nonlinear Dynamics
|July 31, 2015
Summary
This study explores rotational equations of motion using Euler parameters for rigid body dynamics. It demonstrates transformations between different forms and analyzes the Lagrange multiplier and inertia force terms.
Area of Science:
- * Mechanical Engineering
- * Robotics
- * Aerospace Engineering
Background:
- * Three-dimensional rigid body dynamics commonly utilize Euler parameters for rotational coordinates.
- * The inherent dependency of Euler parameters necessitates addressing the quaternion constraint in equations of motion.
- * The Lagrange multiplier technique is a standard approach for handling these constraints.
Purpose of the Study:
- * To derive and analyze various forms of rotational equations of motion for rigid bodies using Euler parameters.
- * To investigate the transformations between these different formulations.
- * To examine the significance of the Lagrange multiplier and the complexity of inertia force terms.
Main Methods:
- * Derivation of rotational equations of motion incorporating the quaternion constraint.
- * Application of the Lagrange multiplier technique.
- * Analysis of mathematical transformations between different equation forms.
Main Results:
- * Demonstrated that various forms of rotational equations of motion are transformable into one another.
- * Provided detailed analysis of the Lagrange multiplier's value and the complexity of inertia force terms.
- * Highlighted the non-uniqueness of the generalized external force vector when using Euler parameters.
Conclusions:
- * The study offers a comprehensive analysis of rotational dynamics using Euler parameters.
- * Understanding the transformations and complexities is crucial for accurate modeling.
- * The non-uniqueness of the generalized external force vector requires careful consideration in applications.
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