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From: Dan Thatcher on 25 Jun 2010 06:32
Hi everyone,

I am trying to build a model of a car accelerating from standstill over a 0.5 seconds time duration in millisecond intervals. For now I am only concerned with the angular displacement, angular velocity and angular acceleration of the body. I have a working model in Excel and am now trying to do the same in Matlab, with little success!

The equations used are the simple equations of motion:
θ=(ω1)t+0.5*α(t^2)
ω2=ω1+αt
α=T/I
Sprung Moment (Ms)=2θ((kwf x L12)+(kwr x L22))
Damping Moment (Md)=2θ((Cwf x L12)+(Cwr x L22))
Nett Applied Moment=Total Overturning Moment of the body– Ms – Md

where, Overturning moment=Sprung mass*acceleration*CofG height (assumed constant)
Kwf=Front spring rate
Kwr=Rear spring rate
Cwf and Cwr=Front and Rear damping rates.

But for the 1st millisecond all the equations must be processed to form a reference for the next millisecond and so on:

%Initial Conditions
s=0; %angular displacement
v=0; %angular velocity
acc=Mo/I; %angular acceleration
Md=0; %Damping moment
Ms=0; %Sprung moment
Mn=Mo; %Nett moment
t=0.001; %time interval

for i=0:0.001:0.5
s(i+1)=(v(i)*(t))+(0.5*acc(i)*(t)^2);
st(i+1)=cumsum(s(i));
v(i+1)=v(i)+(acc(i)*t);
Md(i+1)=2*((Cf*x^2)+(Cr*x1^2))*v(i);
Ms(i+1)=2*((kf*x^2)+(kr*x1^2))*st(i);
Mn(i+1)=Mo-Md(i+1)-Ms(i+1);
acc(i+1)=I/Mn(i+1);
end

I am aware that there will be some basic errors with this as I am still very much a beginner with Matlab, to be honest I'm not even sure if using a for loop is the right way to approach this. The model runs if 'i=1:1:500' but the results are wrong.

I hope this is clear and any help would be much appreciated.
From: us on 25 Jun 2010 07:10
"Dan Thatcher"
> for i=0:0.001:0.5
> s(i+1)=(v(i)*(t))+(0.5*acc(i)*(t)^2);
> end
>
> I am aware that there will be some basic errors with this as I am still very much a beginner with Matlab, to be honest I'm not even sure if using a for loop is the right way to approach this. The model runs if 'i=1:1:500' but the results are wrong.
>
> I hope this is clear and any help would be much appreciated.

well... a typical unhealthy mix of a timing var (your loop indexer) and an index var...

a hint:
- consider something like this and rewrite your loop accordingly

tvec=0:.1:1;
nt=numel(tvec);
s=zeros(1,nt);
s(1)=1;
for i=2:nt % <- loop index
s(i)=tvec(i).*s(i-1); % <- a stupid example to show the various elements...
end

us
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