无表情
发表于 2025-3-30 10:47:32
https://doi.org/10.1007/978-3-642-85278-7rs appear in the expression for the adiabatic invariants. We now wish to begin to locally remove such resonances by trying, with the help of a canonical transformation, to go to a coordinate system which rotates with the resonant frequency.
UTTER
发表于 2025-3-30 14:19:15
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欺骗手段
发表于 2025-3-30 20:10:11
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MAOIS
发表于 2025-3-30 22:26:22
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规范就好
发表于 2025-3-31 01:09:24
Jacobi Fields, Conjugate Points,particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space. If we parametrize the path between points . and . by ϑ, then Jacobi’s princi
细查
发表于 2025-3-31 08:55:47
Action-Angle Variables,, ..) is the generator of a canonical transformation to new constant momenta .., (all .., are ignorable), and the new Hamiltonian depends only on the ..,: . = . = .(..). Besides, the following canonical equations are valid:
青少年
发表于 2025-3-31 09:40:08
Time-Independent Canonical Perturbation Theory, conservative, ∂./∂. = 0, and periodic in both the unperturbed and perturbed case. In addition to periodicity, we shall require the Hamilton-Jacobi equation to be separable for the unperturbed situation. The unperturbed problem ..(..) which is described by the action-angle variables .. and .. will b
漫不经心
发表于 2025-3-31 17:03:52
Removal of Resonances,rs appear in the expression for the adiabatic invariants. We now wish to begin to locally remove such resonances by trying, with the help of a canonical transformation, to go to a coordinate system which rotates with the resonant frequency.
亚麻制品
发表于 2025-3-31 21:27:39
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种族被根除
发表于 2025-4-1 01:44:08
The KAM Theorem,rator .(.,., ..) converges (according to Newton’s procedure) and thus the invariant tori are not destroyed. The KAM theorem is valid for systems with two and more degrees of freedom. However, in the following, we shall deal exclusively with the case of two degrees of freedom.