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The "stationary potential energy" condition for static equilibrium in...
I've often read that, for a mechanical system which can be described by $n$ generalized coordinates $q_1,...,q_n$, a point $\mathbf{Q}=(Q_1,...,Q_n)$ is a point of equilibrium if and only if the...
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Notice that $A$ is a linear operator on $\mathbb R^n$. Suppose that $A$ is singular, namely $\det A= 0$, then the kernel of $A$ is nontrivial. In other words, there exists some nonzero $v\in\mathbb...
View ArticleAnswer by Valter Moretti for The "stationary potential energy" condition for...
Your question actually is one of the most important questions in analytic mechanics. This is because, when you explicitly write the Eulero-Lagrange equations for any constrained system with $n$ degrees...
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