I am learning Hamiltonian and Lagrangian mechanics and looking for a book that starts with Newtonian mechanics and then onto Lagrangian & Hamiltonian mechanics. It should have some historical context explaining the need to change the approaches for solving equation of motions. Also it should explain how all approaches are equivalent to each other intuitively. Also since it requires lot of calculus, recommend a book that has the required math for it too. Thank you!