Recent trends in the Lagrange equation's conversion and form from inertial system to non-inertial system, the application of energy theorem, energy conservation law, etc. are introduced.

Due to increasing consumption of non-renewable energy like petroleum and the urgency of improving the ecological environment, energy conservation became a hot topic in the world.

The paper discusses how to use the principle of conversion between work and potential energy and the law of conservation of mechanical energy in the frame of non-initial reference.