Kinematics and Dynamics for Practicing Engineers Lecture 6: Introduction to Kane’s Method for Formulating Equations of Motion

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Abstract:
The most important tasks that any dynamicist must undertake are the formulating of exact, nonlinear equations of motion of systems of interconnected bodies, for without these equations it is not possible to simulate accurately the behavior of the systems in question. However, the classical methods (e.g., those of Newton‐Euler, Lagrange, Hamilton, etc.) for formulating equations of motion require so much labor and can lead to such lengthy equations when one attempts to apply them to the complex systems encountered in the space industry that it is impractical to employ them, and one cannot solve nonexistent equations no matter how powerful a computer one may possess. It is the purpose of this presentation to provide an introduction to Kane’s method, which does not suffer from the shortcomings of the classical methods in that it leads directly, with minimal labor, to equations having the simplest possible form. Moreover, Kane’s method is much easier to teach and to learn than the classical methods, based as it is on straightforward kinematical concepts.

About the Speaker:
The most important tasks that any dynamicist must undertake are the formulating of exact, nonlinear equations of motion of systems of interconnected bodies, for without these equations it is not possible to simulate accurately the behavior of the systems in question. However, the classical methods (e.g., those of Newton‐Euler, Lagrange, Hamilton, etc.) for formulating equations of motion require so much labor and can lead to such lengthy equations when one attempts to apply them to the complex systems encountered in the space industry that it is impractical to employ them, and one cannot solve nonexistent equations no matter how powerful a computer one may possess. It is the purpose of this presentation to provide an introduction to Kane’s method, which does not suffer from the shortcomings of the classical methods in that it leads directly, with minimal labor, to equations having the simplest possible form. Moreover, Kane’s method is much easier to teach and to learn than the classical methods, based as it is on straightforward kinematical concepts.