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Circular orbits of a particle sliding on a frictionless surface of revolution about a vertical axis are unstable below a critical radius if the curvature of the surface satisfies a specified condition. This behavior can be realized in a…
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
Numerical aspects are investigated in ultra-large-scale electronic structure calculation. Accuracy control methods in process (molecular-dynamics) calculation are focused. Flexible control methods are proposed so as to control variational…
This survey article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal…
We show how some geometric elements of the path of a particle moving in a plane -- the osculating circle and its radius of curvature -- can be used to construct the parabolic trajectory of projectiles in motion under gravity.
The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
In this study, we address the challenge of controlling quantum systems under environmental influences using the theory of dynamical invariants. We employ a reverse engineering approach to develop control protocols designed to be robust…
We introduce a reverse engineering approach to drive a RC circuit. This technique is implemented experimentally 1) to reach a stationary regime associated to a sinusoidal driving in very short amount of time, 2) to ensure a fast discharge…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
This paper investigates the robust nonlinear close formation control problem. It aims to achieve precise position control at dynamic flight operation for a follower aircraft under the aerodynamic impact due to the trailing vortices…
Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The influence of out-of-plane and in-plane contact vibrations and temperature on the friction force acting on a sharp tip elastically pulled on a crystal surface is studied using a generalized Prandtl- Tomlinson model. The average friction…
In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance…
Spin-mechanics studies interactions between spin systems and mechanical vibrations in a nanomechanical resonator and explores their potential applications in quantum information processing. In this tutorial, we summarize various types of…