| | 1 | # Pendulum: Comparing Harmonic Oscillator with 4th order Taylor approximation |
| | 2 | |
| | 3 | ### Taylor 4 approximation: phi'' = - g/r * (phi - 1/6 * phi^3) |
| | 4 | # fortunately, the components of orders 0, 2 and 4 are zero |
| | 5 | |
| | 6 | coefficient.1 -> g/r |
| | 7 | coefficient.2 -> 1/6 # set to 0,167 or 0 (for harmonic solution) |
| | 8 | coefficient.3(-1) -> -phi0 |
| | 9 | |
| | 10 | iintegrate phi'' -> -phi' |
| | 11 | iintegrate -phi' -> phi |
| | 12 | IC: -phi0 |
| | 13 | |
| | 14 | multiply phi, phi -> phi^2 |
| | 15 | multiply phi^2, phi -> phi^3 |
| | 16 | invert phi^3 -> -phi^3 |
| | 17 | |
| | 18 | cmultiply 1/6, -phi^3 -> -1/6*phi^3 |
| | 19 | isum phi, -1/6*phi^3 -> -(phi-1/6*phi^3) |
| | 20 | cmultiply -(phi-1/6*phi^3), g/r -> -g/r*(phi-1/6*phi^3) |
| | 21 | assign -g/r*(phi-1/6*phi^3) -> phi'' |
| | 22 | |
| | 23 | output phi -> out.x |
| | 24 | |
| | 25 | ### Harmonic oscillator: phi'' = - g/r * phi |
| | 26 | coefficient.5 -> g/r_h # identical to g/r |
| | 27 | coefficient.7(-1) -> -phi0_h # identical to -phi0 |
| | 28 | |
| | 29 | iintegrate phi_h'' -> -phi_h' |
| | 30 | iintegrate -phi_h' -> phi_h |
| | 31 | IC: -phi0_h |
| | 32 | invert phi_h -> -phi_h |
| | 33 | |
| | 34 | cmultiply -phi_h, g/r_h -> -g/r*phi_h |
| | 35 | assign -g/r*phi_h -> phi_h'' |
| | 36 | |
| | 37 | output phi_h -> out.y |
projects / Analog_Engine.git / blame_incremental