ABSTRACT
This chapter presents an alternative way of formulating physics problems. This new method was first published by French-Italian mathematician Joseph-Louis Lagrange in 1788 and is therefore called Lagrangian dynamics. Lagrange’s formulation uses a function called the Lagrangian, which is found using the particle’s energy. One advantage of the Lagrangian formulation is that it is the same, regardless of the coordinate system being used. Lagrangian dynamics uses the Euler equation to derive a particle’s equation of motion and the Euler equation takes the same form regardless of the coordinate system being used. Another advantage of Lagrangian dynamics is that it eliminates the need of knowing constraint forces. The chapter discusses how to use the Lagrangian to derive another quantity called the Hamiltonian, which can also be used to derive a particle’s equations of motion. The Hamiltonian’s value extends well beyond the field of classical mechanics and is the central quantity used to describe a particle’s wave function in quantum mechanics.
