Physics · Classical Mechanics
Consider a dynamical system with the Lagrangian function L(q, q̇) = T - U, where the kinetic energy T = a(q)q̇ 2 ≥ 0 and the potential energy U := U(q) with a(q) > 0. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The point (q 0 , q̇ 0 ) is an equilibrium position of the dynamical system if and only if q̇ 0 = 0 and ∂U ∂q | q=q 0 > 0
- 2The point (q 0 , q̇ 0 ) is an equilibrium position of the dynamical system if and only if q̇ 0 = 0 and ∂U ∂q | q=q 0 = 0✓
- 3The point (q 0 , q̇ 0 ) is an equilibrium position of the dynamical system if and only if q̇ 0 = 0 and U(q 0 ) = 0
- 4The associated Lagrange's equation is d dt ( ∂L ∂q ) = ∂L ∂q̇
Correct answer
The point (q 0 , q̇ 0 ) is an equilibrium position of the dynamical system if and only if q̇ 0 = 0 and ∂U ∂q | q=q 0 = 0
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