Helicopter retrieval of stranded fishermen Simple pendulum with time-dependent length (Also "why sucking spaghetti makes a mess")

 The figures to the right show a rescue bucket rigidly connected   to the distal end of a straight cable whose length shortens (retrieval) with a known function   L = 50 - 2*t. The angle q between the cable and the local vertical is governed by physics that yield the nonlinear ODE:
 q''   =   [-2 * L' * q'   -   g * sin(q)] / L
where   g = 9.8 m/s2   and initially (t=0):   q = 1 deg,   q' = 0.
Note: The prime symbol  '  denotes differentiation with respect to t.

 To   solve   these 2nd-order ODEs in MotionGenesis™, type ```Constant g = 9.8 m/s^2 % Earth's gravitational acceleration Specified L'' % Cable length (changes with time) SetDt( L = 50 - 2*t ) % Set L = 50-2*t, L' = -2, L'' = 0 Variable theta'' = (-2*L'*theta' - g*sin(theta))/L ``` To  Input  initial values and numerical integration parameters, type ```Input theta = 1 deg, theta' = 0 deg/sec Input tFinal = 24.92 sec, tStep = 0.02 sec ```
To  Output and Plot   theta (q) vs. t   while solving the  ODE,   type
```OutputPlot  t sec, theta degrees
ODE()  HelicopterRetrievalODE
```
 Plot with MotionGenesis™ or MATLAB®.
**Note: Commands may be entered from a text file, e.g.,   HelicopterRetrievalODE.txt.
**Note: To auto-generate a MATLAB® file,   change   HelicopterRetrievalODE   to   HelicopterRetrievalODE.m

To   form   equations of motion with MotionGenesis™:
 MotionGenesis commands for   F = m*a MotionGenesis program responses
 MotionGenesis commands for dynamics with Kane's method MotionGenesis program responses
 Enlarge image Enlarge image