Re: Problem with "NA"

[Stephen Montgomery-Smith]

On 02/19/2013 11:37 PM, Terry Duell wrote:
> Hello Stephen,
> 
> On Wed, 20 Feb 2013 14:56:03 +1100, Stephen Montgomery-Smith
> <address@hidden> wrote:
> 
> 
>>
>> I think that a much more likely source of creating NA is in evaluating
>> the right hand side function.  That is, you are solving:
>>
>> dx/dt = f(t,x)
>>
>> I am guessing that f(t,x) is something rather horrible.
>>
>> Look for things like taking square roots of negative numbers when you
>> compute f(t,x).  Or maybe you diagonalize a matrix, and it has repeated
>> eigenvalues, and you use the eigenvectors (which will be non-unique or
>> non-spanning).  Or some other operation of that type.
> 
> Nothing like any of that. Just plain old equations of motion f=ma, where
> the f's are forces due to tyre spring, suspension spring, damper
> velocity etc. Nothing out of the ordinary.

Yes, but you also have constraints.  Like the trailer has to follow the
vehicle.  And you can either do this using Lagrange multipliers (which I
guess you didn't do), or sometimes by resolving forces via components.
The former can result in trying to solve equations that do not have
unique solutions, and the latter you might end up doing something like
dividing by tan(theta), and theta could be zero at some point in time.

I'm not saying this is happening in your case.  But these are the kinds
of problems I have encountered.

(I also find it often more convenient to represent complex systems using
Hamiltonian's equations of motion, or the Euler-Lagrange equations.
These are mathematically equivalent to f=ma, but sometimes it is easier
to see what is going on using them.)