Related papers: Routh reduction for singular Lagrangians
In this paper we introduce the essential Lagrange multiplier and establish the solid mathematical foundation of constrained optimization in Hilbert spaces with sharp results on the mathematical foundation of quadratic-programming based…
This paper gives a contribution to the study of regularity of Lagrangian flows on non-smooth spaces with lower Ricci curvature bounds. The main novelties with respect to the existing literature are the better behaviour with respect to time…
In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization…
In this work, we make two improvements on the staggered grid hydrodynamics (SGH) Lagrangian scheme for modeling 2-dimensional compressible multi-material flows on triangular mesh. The first improvement is the construction of a dynamic local…
Data dependent regularization is known to benefit a wide variety of problems in machine learning. Often, these regularizers cannot be easily decomposed into a sum over a finite number of terms, e.g., a sum over individual example-wise…
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…
This paper analyzes the nonlinear Small-Time Local Controllability (STLC) of a class of underatuated aerial manipulator robots. We apply methods of Lagrangian reduction to obtain their lowest dimensional equations of motion (EOM). The…
In this paper, to fit the multi-scale perturbations, the single-parameter Lie transform perturbation theory given in [Ann Phys, 151 1 (1983)] is generalized to a multi-parameter case, which provides a formal solution of the new Lagrangian…
This paper presents a reduction procedure for nonholonomic systems admitting suitable types of symmetries and conserved quantities. The full procedure contains two steps. The first (simple) step results in a Chaplygin system, described by…
Effective Lagrangians, including those that are spontaneously broken, contain redundant terms. It is shown that the classical equations of motion may be used to simplify the effective Lagrangian, even when quantum loops are to be…
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to…
Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily…
Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\sigma equal…
For Hamiltonian field theories on polysymplectic manifolds with a symmetry group action and a momentum map, we explore the redundancy in a set of necessary conditions that has appeared in the literature, for a generalized version of the…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
The Lagrange-Flux schemes are Eulerian finite volume schemes that make use of an approximate Riemann solver in Lagrangian description with particular upwind convective fluxes. They have been recently designed as variant formulations of…
We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We present a simple algorithm for obtaining the restrictions on the gauge…