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Commit | Line | Data |
---|---|---|
1 | # 2 coupled pendulums | |
2 | # x1'' = -k1*x1 + k*(x2-x1) | |
3 | # x2'' = -k2*x2 - k*(x2-x1) | |
4 | # xi are the displacement of the pendulum to its resting position | |
5 | ||
6 | coefficient.1 -> k1 | |
7 | coefficient.2 -> k2 | |
8 | coefficient.3 -> k | |
9 | coefficient.5(-1) -> -x10 # initial displacement x1 | |
10 | coefficient.6(-1) -> -x20 # initial displacement x2 | |
11 | ||
12 | iintegrate x1'' -> -x1' | |
13 | iintegrate -x1' -> x1 | |
14 | IC: -x10 | |
15 | ||
16 | iintegrate x2'' -> -x2' | |
17 | iintegrate -x2' -> x2 | |
18 | IC: -x20 | |
19 | ||
20 | cmultiply x1, k1 -> k1*x1 | |
21 | cmultiply x2, k2 -> k2*x2 | |
22 | ||
23 | invert x1 -> -x1 | |
24 | isum x2, -x1 -> -(x2-x1) | |
25 | cmultiply -(x2-x1), k -> -k*(x2-x1) | |
26 | ||
27 | isum k1*x1, -k*(x2-x1) -> -k1*x1+k*(x2-x1) | |
28 | assign -k1*x1+k*(x2-x1) -> x1'' | |
29 | invert -k*(x2-x1) -> k*(x2-x1) | |
30 | isum k2*x2, k*(x2-x1) -> -k2*x2-k*(x2-x1) | |
31 | assign -k2*x2-k*(x2-x1) -> x2'' | |
32 | ||
33 | output x1 -> out.x | |
34 | output x2 -> out.y |