StudyBrixFree worksheets, study guides and courses

Physics · Advanced university

Hamilton equation for velocity

For H=p²/(2m)+V(q), momentum is canonical and the potential has no momentum dependence.

Make a worksheet

Method and conditions

For H=p²/(2m)+V(q), momentum is canonical and the potential has no momentum dependence.

q̇ = ∂H/∂p

Worked examples

For H(q,p)=p²/(2×13) + 3q²/2 in SI units, find q̇ at p=54 kg·m/s. Round the final result to 4 decimal places if needed. Answer in m/s.

Differentiate H with respect to p: q̇=p/13.

4.1538 m/s

For H(q,p)=p²/(2×7) + 6q²/2 in SI units, find q̇ at p=-10 kg·m/s. Round the final result to 4 decimal places if needed. Answer in m/s.

Differentiate H with respect to p: q̇=p/7.

-1.4286 m/s

Try it

  1. For H(q,p)=p²/(2×12) + 11q²/2 in SI units, find q̇ at p=73 kg·m/s. Round the final result to 4 decimal places if needed. Answer in m/s.

  2. For H(q,p)=p²/(2×7) + 11q²/2 in SI units, find q̇ at p=20 kg·m/s. Round the final result to 4 decimal places if needed. Answer in m/s.

Check your work

Answers and marking notes
  1. 6.0833 m/s

    Differentiate H with respect to p: q̇=p/12.

  2. 2.8571 m/s

    Differentiate H with respect to p: q̇=p/7.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.