Question

If a co-ordinate is cyclic, Hamiltonian would reduce the number of variables in new formulation by : (a) Four (b) One (c) Two (d) Three​

Answer 1

$\huge\underline\purple{\textbf{Required Answer :-}}$

c) 2

$\underline\green{\textbf{Hope it helps...}}$

Answer 2

Answer:

If a co-ordinate is cyclic, Hamiltonian would reduce the number of variables in new formulation by two.

Explanation:

What is Hamiltonian for Cyclic Coordinates?

• To put it another way, both the Hamiltonian and the Lagrangian have a constant corresponding momentum for cyclic coordinates .
• On the other hand, if a generalised coordinate is absent from the Hamiltonian, the associated generalised momentum $p_k$ is conserved.
• Symmetries and conservation-law elements of the Lagrangian were covered before along with cyclic coordinates.
• $p_x$ is conserved, for instance, if the Lagrangian or Hamiltonian are not dependent on the linear coordinate x.
• The same applies to $\theta$ and p$\theta$
• This principle has been extended to include the relationship between time independence and total energy of a system,

• This means that the Hamiltonian equals total energy if the transformation to generalised coordinates is time independent and the potential is velocity independent. So, option c is correct.

To learn more about velocity, refer:

https://brainly.in/question/1767797

https://brainly.in/question/133291

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