- #1

- 740

- 15

[tex]

y = x^2

[/tex]

I get

[tex]

L = KE - PE = \frac {1}{2} m (\dot x^2 + \dot y^2) - mgy = \frac {1}{2}m \dot x^2 (1+4x^2) - mgx^2

[/tex]

[tex]

\frac {\partial L}{\partial x} = (\frac {1}{2}m \dot x^2)(8x) - 2mgx [/tex]

[tex]

\frac {\partial L}{\partial \dot x} = (m \dot x)(1+4x^2)

[/tex]

From here, no matter how I go about differentiating, I get a velocity-dependent force ( [itex] m \ddot x [/itex] ), which does not seem reasonable to me.

Where exactly is my error?