Pengantar metode hamilton

dibahas metode Hamilton yang dibatasi pada sistem dinamika sederhana yang dimulai dart pendekatan persamaan-persamaan Lagrange selanjdtnya ke persamaan Ha-milton. Dengan meneliti persamaan-persaan gerak alp al ami dibahas met de Hamilton seterusnya den an metode Hamilton diteliti himpunan gerak koheren dan aksi ge3_ombang,akhir¬nya diberikan metode Hamilton dad. am ruang rase

Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints

We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton-Jacobi equation as the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton-Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to non-degenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with non-closed two-forms. Accordingly, the Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac-Hamilton-Jacobi equation can be used to exactly integrate the equations of motion.Comment: 44 pages, 3 figure

On Hamilton decompositions of infinite circulant graphs

The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected 2k-valent infinite circulant graph has a two-way-infinite Hamilton path, there exist many such graphs that do not have a decomposition into k edge-disjoint two-way-infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every 2k-valent connected circulant graph has a decomposition into k edge-disjoint Hamilton cycles. We settle the problem of decomposing 2k-valent infinite circulant graphs into k edge-disjoint two-way-infinite Hamilton paths for k=2, in many cases when k=3, and in many other cases including where the connection set is ±{1,2,...,k} or ±{1,2,...,k - 1, 1,2,...,k + 1}

A Study of Generalized Covariant Hamilton Systems On Generalized Poisson manifold

Since the basic theoretical framework of generalized Hamilton system is not perfect and complete, there are often some practical problems that can not be expressed by generalized Hamilton system. The generalized gradient operator is defined by the structure function on manifold to improve the basic theoretical framework of the whole generalized Hamilton system. The generalized structure Poisson bracket is defined as well on manifolds. The geometric bracket is also given, and the covariant extension form of the generalized Hamilton system directly related to the structure function, the generalized covariance, is further obtained--generalized covariant Hamilton system, It includes thorough generalized Hamiltonian system and S-dynamic system.Comment: 15 page

On covering expander graphs by Hamilton cycles

The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree $\Delta$ satisfies some basic expansion properties and contains a family of $(1-o(1))\Delta/2$ edge disjoint Hamilton cycles, then there also exists a covering of its edges by $(1+o(1))\Delta/2$ Hamilton cycles. This implies that for every $\alpha >0$ and every $p \geq n^{\alpha-1}$ there exists a covering of all edges of $G(n,p)$ by $(1+o(1))np/2$ Hamilton cycles asymptotically almost surely, which is nearly optimal.Comment: 19 pages. arXiv admin note: some text overlap with arXiv:some math/061275