New Physics With The Euler-Lagrange Equation: Going Beyond Newton: On-ramps to Quantum Mechanics, Special Relativity, and Noether Theorems

This book shows that the Euler-Lagrange (E-L) equation points to new physics, such as special relativity, quantum mechanics, electromagnetism, general relativity, and thermodynamics theories, and is likely to point to whatever we may find in Nature, such as dark matter and dark energy, as a general formalism.This work also reviews the E-L equation itself, the Lagrangian and Hamiltonian formalism, Noether theorems and current, conservation laws, including a variety of simple and complex mechanical examples, showing that the E-L equation gives the correct answers compared to Newtonian mechanics, and this work provides the E-L equation with proper justification, going beyond Newtonian mechanics.