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I have finished reading a great book called "The Theoretical Minimum" by Leonard Susskind (a famous string theorist) and George Hrabovsky. It's about classical mechanics but mainly talks about both the Lagrangian formulation and the Hamiltonian formulation of classical mechanics. It is great for beginners in physics or just about anyone. It also reviews the ...


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I think the Hamiltonian is not necessarily the energy for the following reason: you can demonstrate that the Lagrangian may be deduced from the D'alembert principle which is linked to the concept of force, etc. but it may be also deduced from the Hamilton's principle which is a pure mathematical concept applied to physics (a certain quantity has to be an ...


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In the context of a canonical transformation (CT) $$z^I~=~(q^i,p_i)~\longrightarrow ~(Q^j,P_j)~=~Z^J~=~f^J(z,t),$$ the matrix $$\textbf{M}^J{}_I~:=~\frac{\partial Z^J}{\partial z^I}$$ is the Jacobian matrix of the CT. Here the indices $$i,j~\in~\{1,\ldots, n\} \quad\text{and}\quad I,J~\in~\{1,\ldots, 2n\}.$$ If the CCR reads $$ ...



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