3 Lagrange’s Equations of Motion 9 3.1 Lagrange’s Equations Via The Extended Hamilton’s Principle . . . . . . . . . . . . . . . . 9 3.2 Rayleigh’s Dissipation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Kinematic Requirements of Lagrange’s Equation . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Lagrange Equation Examples . . . . . . . . . . . . . . . ...

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrat...

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

This paper provides the explicit expression of investment facing a binding debt ceiling and the explicit expression of the Lagrange multipliers related to the binding debt ceiling constraint. This result allows us to check for misspecification of the parameterizations of these Lagrange multipliers used in Euler investment equations tests during the 1990’s.  2000 Elsevier Science S.A. All right...

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form which can always...

The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly dependent equations are also allowed. Both algorithms use the method of Lagrange multipliers to transform the original SLAE into a positively determined functio...