DogeTheBeast
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- May 20, 2020
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I am a class 12 student who is researching in physics. During the process of modeling a trebuchet, I used Lagrangian mechanics for it. And through the Euler lagrangian equation, I landed upon 2 second order differential equations. The theta and the alpha are functions of time. I have no experience with differential equations. Any inputs will be helpful. All the other variables are constants which i plan to add later.
[MATH]mgl_2sin( θ ) - mgl_3sin( θ-α )- Mg l_1 sin( θ ) - [m l_2^2 \ddot{ θ } + ml_3^2 ( \ddot{θ} -\ddot{α} )+m l_2 l_3 \dot{ α} ( 2 \dot{θ} - \dot{α} ) sin( α ) -m l_2 l_3( 2 \ddot{θ} - \ddot{α} ) cos(α )+ M l_1^2 \ddot{ θ }] = 0[/MATH]
[MATH] m l_2 l_3 \dot{ θ }( \dot{θ} - \dot{α} ) sin (α ) + mgl_3 sin(θ -α ) +ml_3^2( \ddot{θ} - \ddot{α} ) - ml_2 l_3 \ddot{θ } cos( α) + ml_2 l_3 \dot{ θ } \dot{ α }sin ( α ) = 0 [/MATH]
[MATH]mgl_2sin( θ ) - mgl_3sin( θ-α )- Mg l_1 sin( θ ) - [m l_2^2 \ddot{ θ } + ml_3^2 ( \ddot{θ} -\ddot{α} )+m l_2 l_3 \dot{ α} ( 2 \dot{θ} - \dot{α} ) sin( α ) -m l_2 l_3( 2 \ddot{θ} - \ddot{α} ) cos(α )+ M l_1^2 \ddot{ θ }] = 0[/MATH]
[MATH] m l_2 l_3 \dot{ θ }( \dot{θ} - \dot{α} ) sin (α ) + mgl_3 sin(θ -α ) +ml_3^2( \ddot{θ} - \ddot{α} ) - ml_2 l_3 \ddot{θ } cos( α) + ml_2 l_3 \dot{ θ } \dot{ α }sin ( α ) = 0 [/MATH]