Hamilton-System-Energiesystem

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Dynamics analysis and Hamilton energy control of a generalized

A generalized chaotic Lorenz system with hidden attractors is used as the under-control system, and its Hamilton energy is formulated and analyzed. As a practical consideration, the system is

When is the Hamiltonian of a system not equal to its total energy?

In an ideal, holonomic and monogenic system (the usual one in classical mechanics), Hamiltonian equals total energy when and only when both the constraint and Lagrangian are time-independent and generalized potential is absent. So the condition for Hamiltonian equaling energy is quite stringent. Dan''s example is one in which Lagrangian depends

Nonlinear Hamiltonian Systems

The system is used as a model for phononic degrees of freedom in a crystal . Here we are specifically interested in nonlinear systems, e.g., with a force which is a nonlinear function of position. Nonlinearity leads to complex coupled Hamilton''s equations of motion, and is hence a seed for realising chaotic motion.

Introduction to Hamiltonian Dynamical Systems and the N-Body

The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical

NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND

Numerical Method Based on Hamilton System and Symplectic Algorithm 343 J(u,v)= 1 2 xTP fx+ 1 2 t f 0 (xTQx+uTR 1u+vTR2v)dt, Hamilton-Jacobi equation will come down to Riccati differential equation. If time runs to infinity, it will come down to algebraic Riccati equation. 1.2 Hamilton system and symplectic algorithm[6] Hamilton system is a

Port-Hamiltonian Systems · Flavio Ribeiro

The system total energy is given by the sum of kinetic and potential energy: by defining the moment variable:, we can rewrite the energy as: and the dynamic equations become the so-called Hamilton''s equations: If we compute the time rate of the Hamiltonian (energy flow): Notice that if the external force is zero, then the system is

Hamiltonian systems

In fact, the Hamiltonian is often just the total energy in mechanical systems, although this isn''t always the case. Let us for the moment specialize the discussion to planar systems, i.e.

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Hamiltonian Dynamics

In Newtonian mechanics, the dynamics of the system are de ned by the force F, which in general is a function of position r, velocity _r and time t. The dynamics are determined by solving N

Energy conservative stochastic difference scheme for stochastic

stochastic Hamilton dynamical system governed by a stochastic differential equations in which the energy function, i.e. Hamiltonian, becomes a conserved quantity. The scheme is given by an stochastic extension of Greenspan''s scheme which leaves Hamiltonians numer-

Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy s spectrum, the system''s energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system''s total energy.Due to its close relation to the

Hamiltonian Systems

In this chapter we give the overviews of Lagrangian and Hamiltonian systems. The basics of Lagrangian and Hamiltonian mechanics, Hamiltonian flows in phase space,

Hamilton-Systeme: Erklärung & Anwendung

Hamilton-Systeme, benannt nach dem irischen Mathematiker Sir William Rowan Hamilton, sind ein zentraler Bestandteil vieler Bereiche der modernen Wissenschaft. Diese Systeme bilden die Grundlage für das Verständnis und die Beschreibung

Hamilton''s Principle: Derivation & Least Action Example

Hamilton''s Principle – asserts that the path a system takes to go from one state to another is such that the action is stationary (typically a minimum). Hamilton''s Principle Derivation – involves deriving the Euler-Lagrange equations from the action integral, and

The bounded sets, Hamilton energy, and competitive modes for

The bounded sets, Hamilton energy, and competitive 4849 oscillation are presented. We also discuss the calcula-tion of the Hamilton energy function for the chaotic plasma system and its role in determining the dynam-ical behavior of this system. 2.1 Mathematical model The chaotic plasma system was introduced by Rabi-

HAMILTONIAN SYSTEMS

A system of 2n, first order, ordinary differential equations z˙ = J∇H(z,t), J= 0 I −I 0 (1) is a Hamiltonian system with n degrees of freedom. (When this system is non-autonomous, it has n+1/2 degrees of freedom.) Here H is the Hamiltonian, a smooth scalar function of the extended phase space variableszandtimet,the2n×2nmatrixJ iscalledthe

Hamiltonian System

This chapter discusses the Hamiltonian system from the point view of energy flows. After giving the general fundamental equation governing Hamiltonian systems, its energy flow equations as

Hamiltonian systems

At first it seems that Hamilton''s formulation gives only a convenient restatement of Newton''s system---the convenience perhaps most evident in that the scalar function (H(q,p)) encodes all of the information of the (2n) first order dynamical equations. However, a Hamiltonian formulation gives much more than just this simplification. Indeed

Framework for generalized Hamiltonian systems through

We express these conditions in the framework of generalized probabilistic theories, which includes generalizing the definition of energy eigenstates in terms of time

Can Hamilton energy feedback suppress the chameleon chaotic

The dynamical system is improved by adding one new variable associated with Hamilton energy, and the feedback gain for energy is adjusted to find target orbits. The Lyapunov exponent, which is used to discern the emergence of chaos when positive value is approached, is calculated when energy feedback is applied, and the phase portraits are also plotted to

Calculation of Hamilton energy function of dynamical system by

The Helmholtz theorem confirms that any vector field can be decomposed into gradient and rotational field. The supply and transmission of energy occur during the propagation of electromagnetic wave accompanied by the variation of electromagnetic field, thus the dynamical oscillators and neurons can absorb and release energy in the presence of complex

On the dynamical behaviors in fractional-order complex PMSM system

In this section, we present an efficient method for chaos control of FOCPMSM system using Hamilton energy function. Since Hamilton energy is dependent on all variables and initial values and at the same time, the nonlinear dynamic systems need enough energy to keep various dynamical behaviors, therefore, Hamilton energy can be used to control

The bounded sets, Hamilton energy, and competitive modes for

Then, the Hamilton energy function of the new system is calculated by the Helmholtz theorem and the energy feedback controller is designed. Finally, the effectiveness of the controller is verified

Calculation of Hamilton energy function of dynamical system by

As is well known, continuous power supply is helpful to keep the oscillating behavior in the dynamical system. The standard Hamilton energy [33,42,56, 63]

Dynamics analysis and Hamilton energy control of a

2998 A. Xin-lei, Z. Li where a,b,c,d are constants, which can hold the sys- tem (1) different states. 2.1.1 Symmetries System (1) is symmetric under the transformation of (x, y, z) → (−x, −y, z), that is, system (1) is symmetric about z axis, and this characteristic remains the same to

Hamilton energy dependence and quasi-synchronization

It becomes crucial to calculate the Hamilton energy and its evolution when exploring dynamics characters in nonlinear systems. Based on the Helmholtz''s theorem, the Hamilton energy of the HR system in an electric field and the modified Chua''s circuit are calculated and analyzed. Then the energy feedback is used to control the system to the

The bounded sets, Hamilton energy, and competitive modes for

This paper estimates a new ultimate bound set (UBS) for the chaotic system caused by the interaction of the whistler and ion-acoustic waves with the plasma oscillation. The intrinsic Hamilton energy is estimated by using the Helmholtz theorem, and this kind of energy function is the most suitable Lyapunov function to discern its dynamic stability. It is found that

Dynamics analysis and Hamilton energy control of a generalized

At the same time, the Hamilton energy function of the system is given to discuss the energy transform when the system undergoes a series of oscillations. The compositional principle can be used to design a new chaos control method, which is called Hamilton energy control. By numerical simulating, the feedback gain in the present control method

Hamiltonian mechanics

In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, [1] Hamiltonian mechanics replaces (generalized) velocities ˙ used in Lagrangian mechanics with (generalized) momenta.Both theories provide interpretations of classical mechanics and describe the same physical

Hamiltonian function | Classical Mechanics, Lagrangian

Hamiltonian function, mathematical definition introduced in 1835 by Sir William Rowan Hamilton to express the rate of change in time of the condition of a dynamic physical system—one regarded as a set of moving particles. The Hamiltonian of a system specifies its total energy—i.e., the sum of its kinetic energy (that of motion) and its potential energy (that of

Hamiltonian system

The most important principle is the Hamilton–Ostrogradski principle (the principle of stationary action), which directly yields the Lagrange equations (in mechanics); if certain

Hamilton Energy Control for the Chaotic System with Hidden

When −1 − az < 0, system is dissipative converges in exponential form (dv/dt) = e −(−1 − az)t, which means that a volume element with an initial volume V(0) converges to a volume element V(0)e −(−1 − az)t at time t.Therefore, when t → +∞, each small volume element including the trajectories of the system converges to zero at an exponential rate −1 − az.

Hamilton Energy Control for the Chaotic System with

It is found that the Hamilton energy is relative to the firing states of the dynamical system. In a stable state, the energy is also a constant, while a chaotic state is resulting from an

ROBUST CONTROL OF HAMILTON SYSTEM AND APPLICATION TO POWER SYSTEM

Design of effective decentralized robust controller with disturbance attenuation is an important objective 247 is a key problem that is to construct the Hamilton function of the system so as to transform the studied system into the form of a forced Hamilton system, although papers (B.M.J. Maschke, 1998, 1999) propose a method to realize the transformation by

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