Checking the correctness of numerical solutions to equations of motion

• Autorzy: Strzałko, J.
• Języki publikacji: EN

Abstrakty

EN

A method for checking the correctness of numerical solutions to equations of motion for conservative and non-conservative mechanical systems expressed in terms of generalised coordinates has been presented. The suggested method consists in checking the energy level in a system under consideration. An application of the verification method of the solving procedure in numerical computations consists in supplementing equations of motion with an additional differential equation describing changes in the total energy and in tracing time histories of the balance of the energy supplied to the system, produced and dissipated in it, as well as the energy transferred to the surroundings. The equation of the energy balance changes is written by means of a certain function, whose derivative fulfils the condition C(t)=0. The solution accuracy is shown by a time history of the function C(t), which should remain constant versus time. A way the function C(t) is derived for holonomic systems described by Lagrange's equations of the second kind, for systems with kinematic constraints described by Lagrange's equations of the second kind with Lagrange multipliers, as well as by Maggi's equations and canonical equations, is given. The examples of applications presented concern, first of all, models of engineering machines.

Słowa kluczowe

EN

correctness; numerical solution; equations of motion

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 1999
• Tom: Vol. 3, nr 1
• Strony: 57--76
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Strzałko, J.

• Technical University of Łódź Department of Mechanics Stefanowskiego 1/15, 91-924 Łódź, Poland Tel. [phone],