Results 271 to 280 of about 37,717 (312)
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Journal of Mathematical Physics, 1981
It is shown that when a completely integrable Hamiltonian system is perturbed about a particular solution the resulting equations to all orders are completely integrable Hamiltonian systems. Numerous examples are worked out and some new constants for the original system are obtained.
A. M. Roos, K. M. Case
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It is shown that when a completely integrable Hamiltonian system is perturbed about a particular solution the resulting equations to all orders are completely integrable Hamiltonian systems. Numerous examples are worked out and some new constants for the original system are obtained.
A. M. Roos, K. M. Case
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Hamiltonian Systems with Convex Hamiltonians
2004A well-known theorem states that if a level surface of a Hamiltonian is convex, then it contains a periodic trajectory of the Hamiltonian system [142], [147]. In this chapter we prove a more general statement as an application of optimal control theory for linear systems.
Yuri L. Sachkov, Andrei A. Agrachev
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Journal of Mathematical Physics, 1995
The initial-value problem for the dynamical system characterized by the Hamiltonian H=λn∑nj=1 pj+μ∑nj,k=1 (pjpk)1/2 cos[ν(qj−qk)] is solved in completely explicit form, for arbitrary n. A set of matrices is introduced, whose remarkable properties are related to this problem, and also present an interest of their own.
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The initial-value problem for the dynamical system characterized by the Hamiltonian H=λn∑nj=1 pj+μ∑nj,k=1 (pjpk)1/2 cos[ν(qj−qk)] is solved in completely explicit form, for arbitrary n. A set of matrices is introduced, whose remarkable properties are related to this problem, and also present an interest of their own.
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On generalized hamiltonian systems
Acta Mathematicae Applicatae Sinica, 2001It is known that a symplectic form is invariant along the trajectory of a Hamiltonian system. Based on this fundamental property, certain techniques have been developed. The aim of this paper is to extend such an approach to a wider class of dynamical systems, namely, generalized Hamiltonian systems.
Liao Li-Zhi +3 more
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Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1987
Modern developments in hamiltonian dynamics are described, showing the change of view that has occurred in the last few decades. The properties of mixed systems, which exhibit both regular and chaotic motion are contrasted with those of the integrable systems, for which the motion is entirely regular, and of Anosov systems, for which it is almost ...
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Modern developments in hamiltonian dynamics are described, showing the change of view that has occurred in the last few decades. The properties of mixed systems, which exhibit both regular and chaotic motion are contrasted with those of the integrable systems, for which the motion is entirely regular, and of Anosov systems, for which it is almost ...
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Hamiltonian systems with controls
Nonlinear Analysis: Theory, Methods & Applications, 1997A controlled Hamiltonian system is given by the first-order differential equations \[ \dot{x}=H_y(t,x,y,w),\quad \dot{y}=-H_x (t,x,y,w) \] with boundary conditions \(x(0)=x(T)\) and \(y(0)=y(T)\), where \(w\) represents the input or control function taking values in some functional space \(W\). The author proves that, under suitable hypothesis, the set
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SIAM Journal on Mathematical Analysis, 1984
Scaling techniques are very important and powerful means to simplify dynamical problems. In this clearly written survey paper a detailed discussion of scaling of variables for Hamiltonian systems is presented by introducing a series of examples of increasing complexity.
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Scaling techniques are very important and powerful means to simplify dynamical problems. In this clearly written survey paper a detailed discussion of scaling of variables for Hamiltonian systems is presented by introducing a series of examples of increasing complexity.
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On subquadratic Hamiltonian systems
Nonlinear Analysis: Theory, Methods & Applications, 1984In this paper we search for T-periodic solutions of the Hamiltonian system -Jż\(=H_ z(t,z)\) when the period T is prescribed and H(t,z) is only differentiable and ''subquadratic'', i.e. H grows less than \(| z|^ 2\) as \(| z| \to \infty\) uniformly in t. The proofs of theorems are based on variational methods and topological arguments (''linking'').
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On the Hamiltonian Flow of Brake Hamiltonian System
Applied Mechanics and Materials, 2013This paper studies the Hamiltonian flow of the brake Hamiltonian dynamical system on the symmetrical symplectic manifold. By using the transformation law of Hamiltonian diffeomorphisms and the Hamiltonian vectors, this paper describes the characteristics of the Hamiltonian flows and proves that the Hamiltonian flows are invariant under some ...
Da Wei Sun, Jia Rui Liu
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Stability in a Hamiltonian system
Mathematical Notes of the Academy of Sciences of the USSR, 1986A Hamiltonian system (1) \(\dot x_ j=-\partial H/\partial y_ j\), \(\dot y_ j=\partial H/\partial x_ j\) \((j=1,2)\) where \[ Hu(1-u\rho_ 1+2Re(x_ 1+iy_ 1)^{q_ 1}(x_ 2+iy_ 2)^{q_ 2}), \] u\(=\alpha \rho_ 1+\rho_ 2\), \(\rho_ j=x^ 2_ j+y^ 2_ j\), \(q_ j\geq 3\) are integers, \(\alpha =-q_ 2/q_ 1\) is considered. Theorem.
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