I Cartesian velocity and generalized velocity

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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 'Why higher speeds need more power if backward force is the same?'

Thread 'Why higher speeds need more power if backward force is the same?'

Power = Force v Speed Power of my horse = 104kgx9.81m/s^2 x 0.732m/s = 1HP =746W Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same? I understand that if I increase weight, it is hrader for horse to pull at higher speed because now is backward force increased, but don't understand why is harder to pull at higher speed if weight(backward force)...
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