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nonautonomo
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There are 11 letters in NONAUTONOMO ( A1M3N1O1T1U1 )
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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 * * * * Q * → * * R * * * * {\displaystyle Q\to \mathbb {R} } * over * * * * * R * * * * {\displaystyle \mathbb {R} } * . For instance, this is the case of non-autonomous mechanics. * An r-order differential equation on a fiber bundle * * * * Q * → * * R * * * * {\displaystyle Q\to \mathbb {R} } * is represented by a closed subbundle of a jet bundle * * * * * J * * r * * * Q * * * {\displaystyle J^{r}Q} * of * * * * Q * → * * R * * * * {\displaystyle Q\to \mathbb {R} } * . A dynamic equation on * * * * Q * → * * R * * * * {\displaystyle Q\to \mathbb {R} } * is a differential equation which is algebraically solved for a higher-order derivatives. * In particular, a first-order dynamic equation on a fiber bundle * * * * Q * → * * R * * * * {\displaystyle Q\to \mathbb {R} } * is a kernel of the covariant differential of some connection * * * * Γ * * * {\displaystyle \Gamma } * on * * * * Q * → * * R * * * * {\displaystyle Q\to \mathbb {R} } * . Given bundle coordinates * * * * ( * t * , * * q * * i * * * ) * * * {\displaystyle (t,q^{i})} * on * * * * Q * * * {\displaystyle Q} * and the adapted coordinates * * * * ( * t * , * * q * * i * * * , * * q * * t * * * i * * * ) * * * {\displaystyle (t,q^{i},q_{t}^{i})} * on a first-order jet manifold * * * * * J * * 1 * * * Q * * * {\displaystyle J^{1}Q} * , a first-order dynamic equation reads* * * * * q * * t * * * i * * * = * Γ * ( * t * , * * q * * i * * * ) * . * * * {\displaystyle q_{t}^{i}=\Gamma (t,q^{i}).} * For instance, this is the case of Hamiltonian non-autonomous mechanics. * A second-order dynamic equation * * * * * * q * * t * t * * * i * * * = * * ξ * * i * * ... |