Physics · Advanced university
Euler-Lagrange equation for a quartic potential · formula reference
For L=mẋ²/2−ax⁴, the force is −4ax³. This one-dimensional model is conservative.
Formula
For L=mẋ²/2−ax⁴, the force is −4ax³. This one-dimensional model is conservative.
d/dt(∂L/∂ẋ) − ∂L/∂x = 0
Worked example
Use SI-compatible constants in L=12ẋ²/2 − 4x⁴. Find ẍ when x=-2 m. Round the final result to 4 decimal places if needed. Answer in m/s².
Euler-Lagrange gives 12ẍ + 16x³=0. Substitute x=-2.
10.6667 m/s²
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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