The purpose of this study is to investigate a method of tracking moving objects with a moving camera. This method interprets tracking as detection of the surface generated by motion boundaries in the spatio-temporal domain and estimates simultaneously the motion induced by camera movement. The problem is formulated as a Bayesian motion-based partitioning problem in the spatio-temporal domain of...

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton–Jacobi equation as the Dirac–Hamilton–Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the th...

A Lagrange-multiplier-based fictitious-domain method (DLM) for the direct numerical simulation of rigid particulate flows in a Newtonian fluid was presented by Glowinski, Pan, Hesla and Joseph (1999). An important feature of this finite element based method is that the flow in the particle domain is constrained to be a rigid body motion by using a well-chosen field of Lagrange multipliers. The ...

We show that steering control can be chosen to give bistability between parallel and antiparallel collective motion states for a continuous-time kinetic model of two agents moving in the plane with unit speed. Variational methods are used to determine the optimal input to the steering control of one of the agents which leads to switching between these collective states. For any given time inter...

Abstract: This paper addresses a stability analysis problem and synthesis problem for pendulum-like systems with multiple nonlinearities. A method for analysing the Lagrange stability of a pendulum-like system with multiple nonlinearities is proposed. In order to study the synthesis problem, the paper develops an Extended Strict Bounded Real Lemma for unstable systems. A sufficient condition fo...