Trajectory equation Of Motion of underdamped
ClassicalMechanics.DampedHarmonicOscillator.trajectory_equationOfMotion_of_underdamped
Plain-language statement
In the underdamped regime, the selected trajectory satisfies the damped equation of motion.
Exact Lean statement
lemma trajectory_equationOfMotion_of_underdamped (IC : InitialConditions)
(hS : S.IsUnderdamped) :
S.EquationOfMotion (S.trajectory IC)Formal artifact
Lean source
lemma trajectory_equationOfMotion_of_underdamped (IC : InitialConditions) (hS : S.IsUnderdamped) : S.EquationOfMotion (S.trajectory IC) := by rw [S.trajectory_eq_of_underdamped IC hS] have hγ : S.γ = 2 * S.m * S.decayRate := S.gamma_eq_two_mul_m_mul_decayRate have hk : S.k = S.m * (S.decayRate^2 - (-S.angularFrequency^2)) := by rw [S.k_eq_m_mul_ω_sq, S.angularFrequency_sq_of_underdamped hS] ring refine S.exp_decay_smul_equationOfMotion S.decayRate (-S.angularFrequency^2) (S.underdampedBase IC) (by unfold underdampedBase fun_prop) ?_ (S.underdampedBase_acceleration IC hS) hγ hk rw [show ∂ₜ (S.underdampedBase IC) = _ from S.underdampedBase_velocity IC hS] fun_prop- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/ClassicalMechanics/DampedHarmonicOscillator/Solution.lean:427-442
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