# Canonical equations of motion and estimation of parameters in the analysis of impact problems.

http://hdl.handle.net/10150/184490
Title:
Canonical equations of motion and estimation of parameters in the analysis of impact problems.
Author:
Movahedi-Lankarani, Hamid
Issue Date:
1988
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The transient dynamic analysis of constrained mechanical systems may require the solution of a mixed set of algebraic and differential equations of motion. The usual formulation of these equations is expressed in terms of the accelerations of the system components. A canonical form of the equations of motion in terms of the system velocities and the time derivative of the system momenta may be used instead. This is a natural form of the equations in which all the state variables are explicitly expressed, and have the same physical importance. The numerical solution obtained from the canonical equations shows more accuracy and stability, specifically for systems with large and fluctuating forces. For the mechanical systems that undergo an impact, the usual numerical solution of the equations of motion is not valid. Two different methods of analysis of impact problems are presented. In one method, the variations of the impulsive force during the contact period are directly added to the vector of forces in the canonical equations of motion. In the second method, based on the assumption of instantaneous nature of impact, a set of momentum balance-impulse equations is derived by explicitly integrating the canonical equations. These equations are solved at the time of impact for the jump in the system momenta right after impact. Necessary parameters are evaluated for the performance of the two methods of analysis. These parameters include the maximum relative indentation, the maximum contact force, and the coefficient of restitution. The parameters are determined for the collision between two bodies in a system with any general geometric or material properties. The influence of friction modeling in the magnitude and the direction of the total force at the contact surfaces is discussed. The dynamics of a vehicle collision is studied in order to illustrate the efficiency of obtaining a solution to the canonical equations, the simplicity of solving the momentum balance-impulse equations.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Collisions (Physics); Dynamics -- Mathematical models.; Impact.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Aerospace and Mechanical Engineering; Graduate College
Degree Grantor:
University of Arizona
Nikravesh, Parviz E.

DC FieldValue Language
dc.language.isoenen_US
dc.titleCanonical equations of motion and estimation of parameters in the analysis of impact problems.en_US
dc.creatorMovahedi-Lankarani, Hamiden_US
dc.contributor.authorMovahedi-Lankarani, Hamiden_US
dc.date.issued1988en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe transient dynamic analysis of constrained mechanical systems may require the solution of a mixed set of algebraic and differential equations of motion. The usual formulation of these equations is expressed in terms of the accelerations of the system components. A canonical form of the equations of motion in terms of the system velocities and the time derivative of the system momenta may be used instead. This is a natural form of the equations in which all the state variables are explicitly expressed, and have the same physical importance. The numerical solution obtained from the canonical equations shows more accuracy and stability, specifically for systems with large and fluctuating forces. For the mechanical systems that undergo an impact, the usual numerical solution of the equations of motion is not valid. Two different methods of analysis of impact problems are presented. In one method, the variations of the impulsive force during the contact period are directly added to the vector of forces in the canonical equations of motion. In the second method, based on the assumption of instantaneous nature of impact, a set of momentum balance-impulse equations is derived by explicitly integrating the canonical equations. These equations are solved at the time of impact for the jump in the system momenta right after impact. Necessary parameters are evaluated for the performance of the two methods of analysis. These parameters include the maximum relative indentation, the maximum contact force, and the coefficient of restitution. The parameters are determined for the collision between two bodies in a system with any general geometric or material properties. The influence of friction modeling in the magnitude and the direction of the total force at the contact surfaces is discussed. The dynamics of a vehicle collision is studied in order to illustrate the efficiency of obtaining a solution to the canonical equations, the simplicity of solving the momentum balance-impulse equations.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectCollisions (Physics)en_US
dc.subjectDynamics -- Mathematical models.en_US
dc.subjectImpact.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US