Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior

Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity

“…Recently contact Hamiltonian mechanics has gained some interest [3][4][5]. In this paper we used a simple contact Hamiltonian to account for quadratic dependence on velocity.…”

“…Ref. [4] studied variational aspects of contact Hamiltonian mechanics and ref. [5] applied contact geometric methods to a theory of gravity called shape dynamics [6][7][8] (see ref.…”

Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

“…Contact geometry was introduced in Sophus Lie's study of differential equations, and has been the subject of intense research, especially related to low-dimensional topology [8]. In recent years, contact Hamiltonian systems have found many applications, first in the context of thermodynamics [9][10][11] and, more recently, in the context of the Hamiltonisation of several dissipative dynamical systems [12][13][14][15][16][17][18][19]. The large number of applications of contact systems that have appeared recently motivated research on geometric numerical integration [15,16,20,21].…”

Contact Hamiltonian Description of 1D Frictional Systems

“…In that paper, authors have focused on the major features of standard symplectic Hamiltonian dynamics and they have showed that all of them can be generalized to the contact case. Later, in Liu's work, the connections between the notions of Hamiltonian system, contact Hamiltonian system and nonholonomic system from the perspective of differential equations and dynamical systems have been described [8]. Also in [9], Dündar has provided a simple contact Hamiltonian description of a system with exponentially vanishing (or zero) potential under a friction term that is quadratic in velocity.…”