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acceleration of system of ODE


acceleration of system of ODE

After a long search story at last I ask here my question.

I had a system of 2nd order constant coeff. linear ODE which describes a reduced geartrain with a motor function.

I used rkadapt to solve the system and obtaiened displacement and velocity plots. My next step was to draw acceleration of gears BUT by using rkadapt I can just obtain angular displacement and velocity. How to plot acceleration of the system. After that I have to investigate spectrum and find out natural frequencies of the system and then making a filter.

Could you guide me please.


Re: acceleration of system of ODE

rk is not as robust as Odesolve and there is about no point using rk

because it's one the Odesolve integrator. With Odesolve, you get

all the functions : the primitive, first and 2nd derivative, which 2nd

derivative is the acceleration, What you get from Odesolve plots

are not exportable functions, only display functions.

For an export, you must approximate the data set from the

Odesolve solutions.



Re: acceleration of system of ODE

... the list shows that I replied twice, not true , only 1.

Click right on Odesove and see the two options:

fixed, adapt ... Odesolve is a numerical solver, it displays

the "lsplined numerical solution", therefore it it not an

export, i.e: it resides on the work sheet , solely.

In the attached example, we solve a 2nd order DE for

3 parameters [m = 1, 25, 50]. The two text box interpolate,

interpolate at ponit or collects a range of interpolated values.

You CAN'T naturally change the built-in lspline Odesolve.

On some project, you might want to see the other pspline,

cspline... There was complaints about that rigidity, here

it is solved: simple elegant . The trick is to pass the internal

vector of solution to a transit local loop. At this point, it is

easy to decide which spline you want to use. The other trick

is to pair the internal vector of solutions with a discretized

vector of the ranged integration variable .

In "S" we collect the 3 parameters [m = 1, 25, 50] solutions

You can collect as many as you want. The text box collects

the solutions you want as governed by the global definition 'j'.

Below, I have added the first and 2nd derivatives plots.

Whether it does help or not in your project, can't tell because

you had no work sheet attached, readable by Mathcad 11.

My point here is more than about solving the given DE, it is

essentially about using the advanced technique of using a

"local transit exploder". This same techique was posted

a day or two ago for collecting functions f(x,y) from a main

vector of user functions for plotting.


I hate that compobox, it should show a dummy vertical

dotted line about where my reply will appear once posted.

All that result from the indenting, a useless invention.

This PTC community is about dead on the number of Mathcad

discusions. Hopefully and for a while the webmaster

reads for all the comments and suggestions that now

have no place where to put them.

Re: acceleration of system of ODE

With a second order system you should have a function (defining the system) giving acceleration as a function of the other variables. Just evaluate that function.