Trajectory equation Of Motion of critically Damped
ClassicalMechanics.DampedHarmonicOscillator.trajectory_equationOfMotion_of_criticallyDamped
Plain-language statement
In the critically damped regime, the selected trajectory satisfies the damped equation of motion.
Exact Lean statement
lemma trajectory_equationOfMotion_of_criticallyDamped (IC : InitialConditions)
(hS : S.IsCriticallyDamped) :
S.EquationOfMotion (S.trajectory IC)Formal artifact
Lean source
lemma trajectory_equationOfMotion_of_criticallyDamped (IC : InitialConditions) (hS : S.IsCriticallyDamped) : S.EquationOfMotion (S.trajectory IC) := by rw [S.trajectory_eq_of_criticallyDamped 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 - 0) := by simpa [sub_zero] using S.k_eq_m_mul_decayRate_sq_of_criticallyDamped hS refine S.exp_decay_smul_equationOfMotion S.decayRate 0 (S.criticallyDampedBase IC) (by unfold criticallyDampedBase fun_prop) (by rw [S.criticallyDampedBase_velocity IC] fun_prop) ?_ hγ hk simpa using S.criticallyDampedBase_acceleration IC- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/ClassicalMechanics/DampedHarmonicOscillator/Solution.lean:409-423
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