Source-pinned research
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This index contains 2,569 research declarations. Search 10,000 more complete Mathlib declarations.
Showing 463 to 468 of 2,569 results.
ClassicalMechanics.DampedHarmonicOscillator.acceleration_eq_of_equationOfMotion
Mathematical statement
Solving the equation of motion for the acceleration: along a solution the second derivative is -(k/m) x - (γ/m) ẋ.
Source project: Physlib
Person-level attribution pending.
ClassicalMechanics.DampedHarmonicOscillator.equationOfMotion_unique
Mathematical statement
Any two smooth solutions of the damped equation of motion with the same initial position and velocity are equal.
Source project: Physlib
Person-level attribution pending.
ClassicalMechanics.DampedHarmonicOscillator.gradLagrangian_eq_force
Mathematical statement
The variational gradient of the Caldirola–Kanai action is the exponential factor times the difference of the force and mass times acceleration appearing in Newton's second law.
Source project: Physlib
Person-level attribution pending.
ClassicalMechanics.DampedHarmonicOscillator.toUndamped_equationOfMotion
Mathematical statement
When γ = 0, the damped equation of motion is equivalent to the equation of motion for the corresponding undamped harmonic oscillator.
Source project: Physlib
Person-level attribution pending.
ClassicalMechanics.DampedHarmonicOscillator.trajectory_equationOfMotion_of_criticallyDamped
Mathematical statement
In the critically damped regime, the selected trajectory satisfies the damped equation of motion.
Source project: Physlib
Person-level attribution pending.
ClassicalMechanics.DampedHarmonicOscillator.trajectory_equationOfMotion_of_overdamped
Mathematical statement
In the overdamped regime, the selected trajectory satisfies the damped equation of motion.
Source project: Physlib
Person-level attribution pending.