БІРӨЛШЕМДІ КОНСЕРВАТИВТІ ЖҮЙЕНІ ЗЕРТТЕУ ӘДІСІ

Abstract

The article examines the movements of systems with equal degrees of freedom in a potential, stationary external field using the laws of theoretical mechanics. In order to study the system, the following generalized form of the Lagrange function was used [1,2]:

If the force F acting on a particle depends only on the x coordinate, the Lagrange function is transformed as follows [1,2]:

где, ,

, .

We have written down the Lagrange equation for plane mathematical, physical, and cyclonic pendulums as follows [3,4]:

+mgl

где, ,

+mg l

The moment of inertia compared to the axis of rotation J, the distance to the center of mass with the axis of rotation l, for the case under consideration ,  J

 , .

For any conservative system, the law of conservation is respected:

The motion of a particle in one-dimensional space is investigated using the Lagrange function and the laws of conservation of energy.