- #1
DannyS
- 3
- 0
I am trying to input these 2 equations of motion for a double acting pendulum into mathematica in hopes of solving for θ2, θ2', and θ2''. I am fairly new to the program and I am having trouble inputting the equations. I am swinging a prosthetic leg like a pendulum and I am trying to predict what the second angle (θ2) will be. Can someone please tell me what I am doing wrong?
1. θ1'' = −g (2 m1 + m2) sin θ1 − m2 g sin(θ1 − 2 θ2) − 2 sin(θ1 − θ2) m2 (θ2'2 L2 + θ1'2 L1 cos(θ1 − θ2))/L1 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))
NDSolve[Subscript[\[Theta], 1]''[
t] == [[\[Minus]9.8*[ Subscript[m, 1] + Subscript[m, 2]]*
sin [Subscript[\[Theta], 1][t]]] \[Minus] [
Subscript[m, 2]*9.8*
sin[Subscript[\[Theta], 1][t] \[Minus]
2 Subscript[\[Theta], 2][t]]] \[Minus] [2*
sin[Subscript[\[Theta], 1][t] \[Minus]
Subscript[\[Theta], 2][t]]* Subscript[m,
2]*[(Subscript[\[Theta], 2]'[t])^2 Subscript[L,
2] + (Subscript[\[Theta], 1]'[t])^2*2* Subscript[L, 1]*
cos[Subscript[\[Theta], 1][t] \[Minus]
Subscript[\[Theta], 2][t]]]/[
Subscript[L,
1] (2*Subscript[m, 1] +
Subscript[m, 2] \[Minus]
Subscript[m, 2] *
cos (2*Subscript[\[Theta], 1][t] \[Minus]
2*Subscript[\[Theta], 2][t]))],
Subscript[\[Theta], 1][0] == 0,
Subscript[\[Theta], 2][0] == 0, (Subscript[\[Theta], 1],
Subscript[\[Theta], 2]), {t, 0, 10}]]]
2. θ2'' = 2 sin(θ1 − θ2) (θ1'2 L1 (m1 + m2) + g(m1 + m2) cos θ1 + θ2'2 L2 m2 cos(θ1 − θ2))/L2 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))
NDSolve[Subscript[\[Theta], 2]''] == [[
2*sin ((\[Pi]/6)*sin (55*[t]) - Subscript[\[Theta],
2])]*[(c)^2*1.61*.3 + [
9.8*1.61*
cos ((\[Pi]/6)*sin (55*[t]))]] + [(Subscript[\[Theta],
2]')^2*0.48*1.61*
cos ( (\[Pi]/6)*cos (55*[t]) - Subscript[\[Theta], 2])]/[
0.48*(1.61 - (1.61*
cos ((2*(\[Pi]/6)*cos (55*[t])) - (2*Subscript[\[Theta],
2]))))]]
I also attached the first equation with the numbers plugged in. I am using the equations of motion found here http://www.myphysicslab.com/dbl_pendulum.html This is the final step to completing my thesis so any help offered is much appreciated. Thank you in advanced.
1. θ1'' = −g (2 m1 + m2) sin θ1 − m2 g sin(θ1 − 2 θ2) − 2 sin(θ1 − θ2) m2 (θ2'2 L2 + θ1'2 L1 cos(θ1 − θ2))/L1 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))
NDSolve[Subscript[\[Theta], 1]''[
t] == [[\[Minus]9.8*[ Subscript[m, 1] + Subscript[m, 2]]*
sin [Subscript[\[Theta], 1][t]]] \[Minus] [
Subscript[m, 2]*9.8*
sin[Subscript[\[Theta], 1][t] \[Minus]
2 Subscript[\[Theta], 2][t]]] \[Minus] [2*
sin[Subscript[\[Theta], 1][t] \[Minus]
Subscript[\[Theta], 2][t]]* Subscript[m,
2]*[(Subscript[\[Theta], 2]'[t])^2 Subscript[L,
2] + (Subscript[\[Theta], 1]'[t])^2*2* Subscript[L, 1]*
cos[Subscript[\[Theta], 1][t] \[Minus]
Subscript[\[Theta], 2][t]]]/[
Subscript[L,
1] (2*Subscript[m, 1] +
Subscript[m, 2] \[Minus]
Subscript[m, 2] *
cos (2*Subscript[\[Theta], 1][t] \[Minus]
2*Subscript[\[Theta], 2][t]))],
Subscript[\[Theta], 1][0] == 0,
Subscript[\[Theta], 2][0] == 0, (Subscript[\[Theta], 1],
Subscript[\[Theta], 2]), {t, 0, 10}]]]
2. θ2'' = 2 sin(θ1 − θ2) (θ1'2 L1 (m1 + m2) + g(m1 + m2) cos θ1 + θ2'2 L2 m2 cos(θ1 − θ2))/L2 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))
NDSolve[Subscript[\[Theta], 2]''] == [[
2*sin ((\[Pi]/6)*sin (55*[t]) - Subscript[\[Theta],
2])]*[(c)^2*1.61*.3 + [
9.8*1.61*
cos ((\[Pi]/6)*sin (55*[t]))]] + [(Subscript[\[Theta],
2]')^2*0.48*1.61*
cos ( (\[Pi]/6)*cos (55*[t]) - Subscript[\[Theta], 2])]/[
0.48*(1.61 - (1.61*
cos ((2*(\[Pi]/6)*cos (55*[t])) - (2*Subscript[\[Theta],
2]))))]]
I also attached the first equation with the numbers plugged in. I am using the equations of motion found here http://www.myphysicslab.com/dbl_pendulum.html This is the final step to completing my thesis so any help offered is much appreciated. Thank you in advanced.