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In mathematics, an autonomous system is a dynamic equation on a smooth manifold. A non-autonomous system is a dynamic equation on a smooth fiber bundle over . For instance, this is the case of non-autonomous mechanics. An r-order differential equation on a fiber bundle is represented by a closed subbundle of a jet bundle of . A dynamic equation on is a differential equation which is algebraically solved for a higher-order derivatives. For instance, this is the case of Hamiltonian non-autonomous mechanics. A second-order dynamic equation

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  • Non-autonomous system (mathematics) (en)
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  • In mathematics, an autonomous system is a dynamic equation on a smooth manifold. A non-autonomous system is a dynamic equation on a smooth fiber bundle over . For instance, this is the case of non-autonomous mechanics. An r-order differential equation on a fiber bundle is represented by a closed subbundle of a jet bundle of . A dynamic equation on is a differential equation which is algebraically solved for a higher-order derivatives. For instance, this is the case of Hamiltonian non-autonomous mechanics. A second-order dynamic equation (en)
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  • In mathematics, an autonomous system is a dynamic equation on a smooth manifold. A non-autonomous system is a dynamic equation on a smooth fiber bundle over . For instance, this is the case of non-autonomous mechanics. An r-order differential equation on a fiber bundle is represented by a closed subbundle of a jet bundle of . A dynamic equation on is a differential equation which is algebraically solved for a higher-order derivatives. In particular, a first-order dynamic equation on a fiber bundle is a kernel of the covariant differential of some connection on . Given bundle coordinates on and the adapted coordinates on a first-order jet manifold , a first-order dynamic equation reads For instance, this is the case of Hamiltonian non-autonomous mechanics. A second-order dynamic equation on is defined as a holonomicconnection on a jet bundle . Thisequation also is represented by a connection on an affine jet bundle . Due to the canonicalembedding , it is equivalent to a geodesic equationon the tangent bundle of . A free motion equation in non-autonomous mechanics exemplifies a second-order non-autonomous dynamic equation. (en)
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