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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · ODE, PDE & Applied Mathematics › Classical Mechanics

“The generalised momentum ∂L/∂q̇ always equals mass × velocity” — false

Counterexample locked — unlock with Notes + PYQ

mechanics

#2 · ODE, PDE & Applied Mathematics › Classical Mechanics

“The Hamiltonian always equals the total energy” — false

Counterexample: 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.

mechanics