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Re: [Phys-L] Curve Fitting




On 2012, Aug 29, , at 13:01, John Clement wrote:


This problem has been with us since Newton. He fully understood algebra,
but distrusted it because it hid understanding.

This also explains Hook's use of geometry for his study of orbits? Balmer also used geometry.


This brings up one of my complaints about texts that discuss mechanical oscillators, Very few explicitly show that the dissipation coefficient includes the mass -- especially in the case of the pendulum where it cancels in the position (angle). The best creation of the diff. eq. for the pendulum I have is a maths text. It begins w/ torques simplifies the moment of inertia and lastly uses the small angle approximation.

Regarding fitting: Peter Scott an early, if not a founding, member of the UCSC Physics Department devotes fifteen pp. to his Marquardt algorithm, including:

fitting curves nonlinear in the parameters: the Marquardt algorithm
the general idea
the taylor expansion method
the gradient method
the Marquardt method
the finer details
scaling
testing for convergence
confidence limits
the correlation matrix

general references

http://physics.ucsc.edu/~drip/133.html


The advanced lab. students must write their own modules in c including the coefficient partials.

bc