MotionGenesis: F=ma Software, textbooks, training, consulting.
Problem statement (.pdf)
   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:
  MotionGenesis Helicopter Retrieval Pendulum
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
MotionGenesis Helicopter Retrieval (pendulum with time-dependent length)
MotionGenesis Helicopter Retrieval (pendulum with time-dependent length)
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
MotionGenesis Helicopter Retrieval Pendulum MotionGenesis Helicopter Retrieval Pendulum
Enlarge image Enlarge image