Matches in DBpedia 2014 for { ?s ?p In mathematics, 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 canonicalimbedding , 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.. }
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- Non-autonomous_system_(mathematics) abstract "In mathematics, 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 canonicalimbedding , 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.".