Conservation of Total Energy

This lecture explains how total energy is conserved in systems where the potential energy function is not explicitly dependent on time. The instructor demonstrates that the total energy remains constant by analyzing the time derivatives of kinetic and potential energy. The concept of conservative dynamics and forces is explored, along with the application of the chain rule to show the conservation of energy. The lecture also discusses how energy conservation can be used to verify the accuracy of numerical integration schemes, emphasizing the importance of monitoring total energy fluctuations. The instructor concludes by highlighting the significance of energy conservation in classical mechanics and its role as a quality criterion for numerical simulations.