Is the following statement true? The Hamiltonian always equals the total energy

No. A bead on a wire rotating at forced angular velocity ω The constraint is time-dependent, so H is conserved but differs from T + V.

Counterexample

Is this true?

The Hamiltonian always equals the total energy

No — it is false.

The counterexample

A bead on a wire rotating at forced angular velocity $\omega$

Why it fails

The constraint is time-dependent, so H is conserved but differs from T + V.

Keep practicing

Execution slip

The idea was right. The computation was not.

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.