I Cartesian velocity and generalized velocity

AI Thread Summary
The discussion revolves around a query regarding a specific notation in "A Student's Guide to Lagrangians and Hamiltonians" by Patrick Hamill, specifically whether to use ##\delta_{kj}## instead of ##\delta_{ij}## in the context of generalized velocity. Participants agree that the notation should indeed be ##\delta_{kj}##. The conversation is brief, with a focus on clarifying this point in the text. The consensus reinforces the importance of accurate notation in understanding the material. Overall, the discussion emphasizes the need for precision in mathematical expressions within the book.
beowulf.geata
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Hi,

I'm reading A Student's Guide to Lagrangians and Hamiltonians by Patrick Hamill and, in the following section on generalized velocity, I'm wondering if we should have ##\delta_{kj}## rather than ##\delta_{ij}##?

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Many thanks.
 
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beowulf.geata said:
Hi,

I'm reading A Student's Guide to Lagrangians and Hamiltonians by Patrick Hamill and, in the following section on generalized velocity, I'm wondering if we should have ##\delta_{kj}## rather than ##\delta_{ij}##?
Looks like it.
 
PeroK said:
Looks like it.
Many thanks!
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

This argument is another version of my previous post. Imagine that we have two long vertical wires connected either side of a charged sphere. We connect the two wires to the charged sphere simultaneously so that it is discharged by equal and opposite currents. Using the Lorenz gauge ##\nabla\cdot\mathbf{A}+(1/c^2)\partial \phi/\partial t=0##, Maxwell's equations have the following retarded wave solutions in the scalar and vector potentials. Starting from Gauss's law $$\nabla \cdot...
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