- #1
nomadreid
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From "A Student's Guide to Langrangins and Hamiltonians", Patrick Hamill, Cambridge, 2017 edition.
Apologies: since I do not know how to put dots above a variable in this box, I will put the dots as superscripts. Similarly for the limits in a sum.
On page 6,
"we denote the coordinates by qi and the corresponding velocities by q⋅i."
Further he terms pi the generalized momenta.
Then, on page 97, using L as the Lagrangian,
" H(qi, pi, t) = ∑i=1npiq⋅i - L(qi, q⋅i,t)" [equation (4.8)]
The function H is called the Hamiltonian...Keep in mind that the Hamiltonian must be expressed in terms of the generalized momentum. An expression for H involving velocities is wrong." (Italics in the original.)
But it is not clear to me why equation 4.8 is not also in terms of velocities, i.e., q⋅i
(Perhaps this should be a mathematics threads rather than a QM thread; I place it here because of the context.)
Apologies: since I do not know how to put dots above a variable in this box, I will put the dots as superscripts. Similarly for the limits in a sum.
On page 6,
"we denote the coordinates by qi and the corresponding velocities by q⋅i."
Further he terms pi the generalized momenta.
Then, on page 97, using L as the Lagrangian,
" H(qi, pi, t) = ∑i=1npiq⋅i - L(qi, q⋅i,t)" [equation (4.8)]
The function H is called the Hamiltonian...Keep in mind that the Hamiltonian must be expressed in terms of the generalized momentum. An expression for H involving velocities is wrong." (Italics in the original.)
But it is not clear to me why equation 4.8 is not also in terms of velocities, i.e., q⋅i
(Perhaps this should be a mathematics threads rather than a QM thread; I place it here because of the context.)