Cartesian velocity and generalized velocity

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SUMMARY

The discussion centers on the interpretation of generalized velocity in the context of Lagrangian mechanics as presented in "A Student's Guide to Lagrangians and Hamiltonians" by Patrick Hamill. Participants debate whether the correct notation should be ##\delta_{kj}## instead of ##\delta_{ij}## when discussing the properties of generalized velocity. The consensus indicates that ##\delta_{kj}## is indeed the appropriate choice, affirming the importance of precise notation in theoretical physics.

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  • Understanding of Lagrangian mechanics
  • Familiarity with Hamiltonian dynamics
  • Knowledge of tensor notation and Kronecker delta
  • Basic concepts of generalized coordinates and velocities
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  • Study the implications of generalized velocity in Lagrangian mechanics
  • Explore the role of Kronecker delta in tensor calculus
  • Review examples of Lagrangian and Hamiltonian systems
  • Investigate common notational conventions in theoretical physics
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Students of physics, particularly those studying classical mechanics, as well as educators and researchers focusing on Lagrangian and Hamiltonian formulations.

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}##?

7.jpg


8.jpg


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!
 

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