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Physics · Advanced university

Poisson bracket of two monomials

Use the declared order; reversing f and g reverses the bracket sign.

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Method and conditions

Use the declared order; reversing f and g reverses the bracket sign.

{f,g} = f_q g_p − f_p g_q

Worked examples

Using {f,g}=f_q g_p−f_p g_q, calculate {6q², 12p²} at q=-3, p=-5. Treat variables as dimensionless. Round the final result to 4 decimal places if needed.

Only the first product survives: (12q)(24p).

4320

Using {f,g}=f_q g_p−f_p g_q, calculate {5q², 7p²} at q=-3, p=-4. Treat variables as dimensionless. Round the final result to 4 decimal places if needed.

Only the first product survives: (10q)(14p).

1680

Try it

  1. Using {f,g}=f_q g_p−f_p g_q, calculate {4q², 11p²} at q=-2, p=2. Treat variables as dimensionless. Round the final result to 4 decimal places if needed.

  2. Using {f,g}=f_q g_p−f_p g_q, calculate {4q², 7p²} at q=-6, p=1. Treat variables as dimensionless. Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. -704

    Only the first product survives: (8q)(22p).

  2. -672

    Only the first product survives: (8q)(14p).

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