We illustrate a computational approach to practical nonlinear balancing via the forced damped pendulum example.

We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The characteristic feature of this nonlocal system is that it breaks local composition low for the classical Hamiltonian dynamics and the corresponding quan...

1 Problem It is generally considered that systems with friction are not part of Hamiltonian dynamics, but this is not always the case. Show that a (nonrelativistic) damped harmonic oscillator can be described by a Hamiltonian (and by a Lagrangian), with the implication that Liouville's theorem applies here. Consider motion in coordinate x of a particle of mass m with equation of motion, m¨x + β...

Abstract Following the Caldeira-Leggett approach to describe dissipative quantum systems the structure function for a harmonic oscillator with Ohmic dissipation is evaluated by an analytic continuation from euclidean to real time. The analytic properties of the Fourier transform of the structure function with respect to the energy transfer (the “characteristic function”) are studied and utilize...

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum de-coherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations b...

A fundamental issue in locomotion is to understand how muscle forcing produces apparently complex deformation kinematics leading to movement of animals like undulatory swimmers. The question of whether complicated muscle forcing is required to create the observed deformation kinematics is central to the understanding of how animals control movement. In this work, a forced damped oscillation fra...