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fluidistic
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Homework Statement
The problem can be found in L&L's book "Mechanics" in the end of the first chapter. (See the last picture of page 12 of http://books.google.com.ar/books?id...v+Davidovich+Landau"&cd=2#v=onepage&q&f=false ). The mass m1 is free to move on the x-axis. While the mass m2 moves like a pendulum. There's the gravitational acceleration [tex]\vec g[/tex]. I must find the Lagrangian of such a system.
I keep getting [tex]L=\frac{m_1 \dot x ^2}{2}+\frac{m_2 }{2} \left [ \dot x ^2 +2 \dot{\vec x} \dot \theta l \cos (\theta) + \dot \theta ^2 l^2 +2gl \cos (\theta) \right ][/tex]. I see that I have an error: I have a vector [tex]\dot {\vec x }[/tex] which is impossible.
L&L's answer is [tex]L\frac{1}{2} (m_1+m_2) \dot x^2 +\frac{1}{2}m_2 (l^2 \theta ^2 +2l \dot x \theta \cos \theta)+m_2 g l \cos \theta[/tex].
I don't understand what I'm doing wrong. Also L&L don't have any [tex]\dot \theta[/tex] term... Mine appeared when I calculated T_2, the kinetic energy of m_2 in polar coordinates. When I derivated the position [tex]\vec r_2 =(\dot {\vec x} + l \sin \theta )\hat i + (l \cos \theta) \hat j[/tex] with respect to time I got some [tex]\dot \theta[/tex] terms.
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