• To: mathgroup at smc.vnet.net
• Subject: [mg15523] Re: your post
• From: Paula Chammas <chammas at dbag.bln.daimlerbenz.com>
• Date: Mon, 18 Jan 1999 23:47:23 -0500
• References: <199901180804.DAA19895@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

``` Dear All,

At the beginning of December I posted a question regarding NDSolve.
Thanks for all the responses. I managed to solve the problem  using the
following:

NDSolve[{
w'[t] == -2 w[t] + Tin[t] - Sign[w[t] - v[t]] 2/3 Fn[t],
v'[t] == (-v[t] + Sign[w[t] - v[t]] 2/3 Fn[t] )/5, w[0]==0, v[0]==0},
{w,v}, {t, 0, 10}, MaxSteps->40000, AccuracyGoal->2}

given

Tin[t] := -2 t + 12 /; (5 <= t && t <= 6)
Tin[t] := 2 /; (0 <= t && t
<=5)
Tin[t] := 0 /; (6 <= t && t <= 10)

Fn[t] := 0.785 t /; (0 <= t && t <=
2)
Fn[t] := 1.57 /; (2 <= t && t <=5)
Fn[t] := -0.785 t + 5.495 /; (5 <= t && t <= 7)
Fn[t] := 0 /; (7 <= t && t <= 10)

Now the system becomes more involved.

The new system look like the following: 2 clutches C1 and C2 in parallel

w    T1,C1   v
Tin -------||-----  Tout
----m    T2,C2   n------
-------||-----

Tin is input torque, it is given (see below) and Tin = T1 + T2

w, m are input speeds
v,n are ouput speeds

So basically we have 2 sets of equations one for C1 and one for C2:

w'[t] == -2 w[t] + T1[t] - Sign[w[t] - v[t]] 2/3 Fn[t],
v'[t] == ( -v[t]+ Sign[w[t] - v[t]] 2/3 Fn[t] )/5,

m'[t] == -2 m[t] + T2[t] - Sign[m[t] - n[t]] Fn[t],
n'[t] == ( -n[t] + Sign[m[t] - n[t]]  Fn[t] )/5

with the following constraints:

Tin[t] = T1[t] + T2[t]
w[t] = m[t]
v[t] = n[t]
v[0] = w[0] = m[0] = n[0] = 0
{t, 0, 10}

Fn[t], and Tin[t] are given above.

T1 and T2 should be determined by the system

When I try to solve the system it does not like the equation

Tin[t] = T1[t] + T2[t]

I get :
Input is not an ordinary differential equation of T1[t]

and in some cases

NDSolve:: ndsv: Cannot find a starting point of t

What is the best way of formulating the problem using mathematica?

Any ideas?

Thanks in advance and a happy New year to all.

Paula

_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
Paula Chammas
DaimlerChrysler
Research and Technology                  !!NEW Alt-Moabit 96A
Tel: +49 30 39982 376 10559 Berlin             fax: +49 30 39982 107

paula.chammas at daimlerchrysler.com
_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
Experience is a hard  teacher because she gives the test first, the lesson afterward.

```

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