Part CCSIR NET December 2023poisson-bracket-conditions

Poisson bracket conditions

Let $q_{1}, q_{2}$ be generalized coordinates and $p_{1}, p_{2}$ their conjugate momenta. Let a and b be such that $Q_{1} = q_{1}, P_{1} = a p_{1} + 16 p_{2}, Q_{2} = p_{2}, P_{2} = 2 q_{1} + b q_{2}$ is a canonical transformation. Which of the following statements are true?

A. $a^{2} + b^{2} = 2$ ✓
B.a − b = 2✓
C.a + b = 2
D.a = 1, b = 1

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Related counterexample: The Hamiltonian always equals the total energy

The chapter behind this: Hamiltonian mechanics, Poisson brackets and canonical transformations — free to read

From Classical Mechanics › Hamiltonian formalism and conservation laws

ShareWhatsApp Telegram