Alright, thanks both of you. In the context of the level of difficulty of the rest of the problems from that chapter, it seemed far too simple leaving it there, seeming like an incomplete solution. Thanks again.
Hello, thank you.
I took the constraint into account by substituting y=ax^4 and \dot{y}=4ax^3 into the Lagrangian: L = T-V = \frac{1}{2}m(\dot{x}^2 + \dot{y}^2) - mgy
To yield, without any small oscillation approximation: L = \frac{1}{2}m\dot{x}^2 (1+16 a^2 x^6) -mgax^4
However, when you try...
Homework Statement
From Goldstein Classical Mechanics, 6.16:
A mass particle moves in a constant vertical gravitational field along the curve defined by y=ax4 , where y is the vertical direction. Find the equation of motion for small oscillations about the position of equilibrium.
The...