Nonconservative Lagrangian Mechanics: A generalized function approach
نویسندگان
چکیده
We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the Lagrangian framework by treating the action as a Volterra series. It is then possible to derive two equations of motion, one of these is an advanced equation and the other is retarded.
منابع مشابه
Nonconservative Lagrangian mechanics II: purely causal equations of motion
This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A 36, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as ‘time dependent’ Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational princip...
متن کاملOn the Geometrically Nonlinear Analysis of Composite Axisymmetric Shells
Composite axisymmetric shells have numerous applications; many researchers have taken advantage of the general shell element or the semi-analytical formulation to analyze these structures. The present study is devoted to the nonlinear analysis of composite axisymmetric shells by using a 1D three nodded axisymmetric shell element. Both low and higher-order shear deformations are included in the ...
متن کاملA Nonconservative Lagrangian Framework for Statistical Fluid Registration - SAFIRA
In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero ra...
متن کاملGeometrical Interpretation of Constrained Systems
The standard approach to classical dynamics is to form a Lagrangian which is a function of n generalized coordinates qi, n generalized velocities q̇i and parameter τ . The 2n variables qi, q̇i form the tangent bundle TQ. The passage from TQ to the cotangent bundle T ∗Q is achieved by introducing generalized momenta and a Hamiltonian. However, this procedure requires that the rank of Hessian matrix
متن کاملClassical mechanics of nonconservative systems.
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. T...
متن کامل