Help to model a phisical problem in Matlab
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I'm sorry but I'm too rusted to solve this alone. If anyone can help me :)
It’s a physical problem, I have a plastic pipe coming out vertically from an inlet. At the same time the end of the pipe is tied to a wire that is coming out below.
The speed of the output of the plastic pipe and of the wire is proportional and fixed: Vplastic = Ratio * Vwire.
In addition to that there is a point I need the curve to pass by at a certain time as well as the end point at the end of the movement should be on the X axis.
I need to model how the ending point of the plastic tube will evolve through time.
So here is the starting schema:
Here is an example (fake curve… it is what I need to find):
These are the conditions I have:
- Vplastic = Ratio * Vwire
- Vplastic = Length of arc at the end divided by time
- Vwire = Max length divided by time, note that is possible that the PassBy point has a length superior to the final length. In this case the Vwire = Length at PassBy + abs value of (length PassBy – End Length)
- T0 plastic = Point (0, 2) or parametric
- T0 wire = Point (0, 0) or parametric
- Tangent of curve at T0 plastic is vertical
- For any T the length of the arc is proportional to the length of the wire. Is related to point 1)
- Tangent of curve at and point can with any inclination (in the diagram is vertical by chance)
- Tend = Point (0, 26) or parametric.
darova on 25 Aug 2021
Why about spline? I placed two points close to each other to manipulate with tangent angle
x0 = [0 0 2 3 4 4]; % some data
y0 = [0 0.1 2 2 0.1 0];
[t0,r0] = cart2pol(x0-mean(x0),y0); % ceonvert to polar (move the data to center)
t1 = linspace(0,pi); % more points
r1 = spline(t0,r0,t1); % interpolation
[x1,y1] = pol2cart(t1,r1); % convert ot cartesian
x1 = x1+mean(x0); % move new data to original position