The Lagrangian approach requires that you treat the Lagrangian as an abstract function of independent variables. You can't jump ahead, solve the equations of motion, and plug these back into the Lagrangian and start again.Trying2Learn said:Summary:: Lagrangian, Kinetic Energy (where am I going wrong)
I am sorry for all these questions this morning.
Could someone read the attached and tell me where I am going wrong?
Lagrangian is a mathematical function that is used to describe the motion of a system in classical mechanics. It takes into account the kinetic and potential energies of the system and allows for the calculation of the system's equations of motion.
One common mistake is forgetting to account for all of the forces acting on the system. Another is using the wrong coordinate system or not properly defining the system's constraints.
Lagrangian is a more general and elegant approach to describing the motion of a system compared to Newtonian mechanics. It takes into account all of the forces acting on the system, including non-conservative forces, and can be applied to systems with complex geometries.
Yes, Lagrangian can also be used in other areas of science such as quantum mechanics and electromagnetism. It provides a powerful tool for understanding the behavior of systems in these fields.
Practicing with various examples and problems is the best way to improve your understanding and application of Lagrangian. It is also helpful to have a solid understanding of calculus and classical mechanics principles.