Physics · Advanced university
Hamilton equation for velocity · formula reference
For H=p²/(2m)+V(q), momentum is canonical and the potential has no momentum dependence.
Formula
For H=p²/(2m)+V(q), momentum is canonical and the potential has no momentum dependence.
q̇ = ∂H/∂p
Worked example
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
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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