In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function H ∈ C(R,R) is super-quadratic and convex, for every number τ > 0, there exists at least one τ -periodic brake orbit (τ, x) with minimal period τ or τ/2 provided H(Nx) = H(x). §

Abstract This paper consider the existence and multiplicity of solutions for the first order Hamiltonian systems satisfying Sturm-Liouville boundary conditions without convexity assumption. The gradient of Hamiltonian function is generalized asymptotically linear. We find critical points of the corresponding functional by verifying the assumptions of Theorems about critical points given by Bart...

When dissipative terms are dropped, all of the important models of plasma physics are described by partial differential equations that possess Hamiltonian form in terms of noncanonical Poisson brackets. For example, this is the case for ideal magnetohydrodynamics, the Vlasov–Maxwell equations, and other systems see Refs. 7–9 for review . Among these, there exist several reduced fluid models who...

We propose a generalization of Hamiltonian mechanics, as a Hamiltonian inclusion with convex dissipation function. We obtain a dynamical version of the approach of Mielke to quasistatic rate-independent processes. Then we show that a class of models of dynamical brittle damage can be formulated in this setting. MSC 2000: 34G25; 70H05; 74R05

From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of thismodel from the Poisson bracket of the Vlasov equation, andwe discuss the associated Casimir invariants. © 2014 Elsevier Inc. All rights...

In this paper, we consider bifurcation of limit cycles in near-Hamiltonian systems. A new method is developed to study the analytical property of the Melnikov function near the origin for such systems. Based on the new method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Moreover, we consider the case that the Hamiltonian ...

The ∂̄-dressing scheme based on local nonlinear vector ∂̄-problem is developed. It is applicable to multidimensional nonlinear equations for vector fields, and, after Hamiltonian reduction, to heavenly equation. Hamiltonian reduction is described explicitely in terms of the ∂̄-data. An analogue of Hirota bilinear identity for heavenly equation hierarchy is introduced, τ -function for the hierarchy...

This paper shows that any thermodynamic potential fulfilling some thermodynamic stability criterion (e.g. the chemical affinity or the ectropy) can be used as a potential function for the dissipative (pseudo) Port Hamiltonian formulation of the non isothermal Continuous Stirred Tank Reactor (CSTR) model. Besides Brayton-Moser formulation is used to obtain some dissipative Port Hamiltonian repre...

In this paper, a multimachine power system is first represented as the generalized Hamiltonian control system with dissipation. Then, a decentralized saturated steam valving and excitation controller, which is staticly measurable, is proposed based on the Hamiltonian function method. Last, an example of threemachine power system is discussed in detail.

We outline the construction of a proper C2-smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.