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570:{\displaystyle q_{tt}^{i}=d_{t}\Gamma ^{i}+\partial _{j}\Gamma ^{i}(q_{t}^{j}-\Gamma ^{j})-{\frac {\partial q^{i}}{\partial {\overline {q}}^{m}}}{\frac {\partial {\overline {q}}^{m}}{\partial q^{j}\partial q^{k}}}(q_{t}^{j}-\Gamma ^{j})(q_{t}^{k}-\Gamma ^{k}),}
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De Leon, M., Rodrigues, P., Methods of
Differential Geometry in Analytical Mechanics (North Holland, 1989).
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A free motion equation need not exist in general. It can be defined if and only if a configuration bundle
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that describes a mechanical system in the absence of external forces, but in the presence only of an
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853:, Geometric Formulation of Classical and Quantum Mechanics (World Scientific, 2010)
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652:{\displaystyle \Gamma ^{i}=\partial _{t}q^{i}(t,{\overline {q}}^{j})}
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733:. The right-hand side of this equation is treated as an
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28:depending on the choice of a reference frame. In
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223:. Given an arbitrary reference frame
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761:{\displaystyle Q\to \mathbb {R} }
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283:{\displaystyle Q\to \mathbb {R} }
216:{\displaystyle Q\to \mathbb {R} }
85:{\displaystyle Q\to \mathbb {R} }
53:{\displaystyle Q\to \mathbb {R} }
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849:Giachetta, G., Mangiarotti, L.,
92:which is brought into the form
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62:non-autonomous dynamic equation
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255:{\displaystyle (t,q^{i})}
32:on a configuration space
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30:non-autonomous mechanics
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949:–related article is a
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994:Categories
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786:×
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481:∂
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814:See also
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580:where
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863:arXiv
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