Kosambi–Cartan–Chern (KCC) theory for higher-order dynamical systems
نویسندگان
چکیده
منابع مشابه
Nonlinear Dynamical Systems and Kcc - Theory
Nonlinear dynamical systems can be uniquely investigated by a geometric theory (KCC-theory). The five KCC-invariants express intrinsic properties of the nonlinear dynamical systems. The second invariant as a curvature tensor determines the stability of the systems. The third invariant as a torsion tensor expresses the chaotic behavior. As an example, the KCC-theory is applied to a geodynamical ...
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Moment matching theorems for Krylov subspace based model reduction of higherorder linear dynamical systems are presented in the context of higher-order Krylov subspaces. We introduce the definition of a nth-order Krylov subspace Kn k ({Ai} n i=1;u) based on a sequence of n square matrices {Ai}i=1 and vector u. This subspace is a generalization of Krylov subspaces for higher-order systems, incor...
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A fundamental problem in robustness analysis is to determine the ability of a system matrix to maintain its “stability” under a certain class of perturbations. Since the entries of such matrices frequently depend on some physical parameters, it seems natural to consider real perturbations. In many applications it is more convenient to deal with the characteristic polynomial of the (closed-loop)...
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چکیده در این پایاننامه ابتدا فضاهای متریک فازی را به صورت مشاهدهگرایانه بررسی میکنیم. فضاهای متریک فازی و توپولوژی تولید شده توسط این متریک معرفی شدهاند. سپس بر اساس فضاهایی که در فصل اول معرفی شدهاند آشوب توپولوژیکی، مینیمالیتی و مجموعههای متقاطع در شیوههای مختلف بررسی شده- اند. در فصل سوم مفهوم مجموعههای جاذب فازی به عنوان یک مفهوم پایهای در سیستمهای نیم-دینامیکی نسبی، تعریف شده است. ...
15 صفحه اولThe Hamiltonian Formulation of Higher Order Dynamical Systems
Using Dirac’s approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the present analysis yields in a transparent manner the local structure of the associated phase space and its local sympletic geometry, and is of direct application...
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ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2016
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s0219887816500146