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Backward Euler Finite-Difference Equation for a Force-Driven Mass
Newton's
can be written in terms of
force
and
velocity
or
momentum
as
The backward-difference substitution gives
for
. Or, in a lighter notation,
with
We often use a ``hat'' to denote
approximation:
In this case,
is more accurately written as
Solving for
yields a
difference equation
(
finite difference scheme
):
with
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Download
DigitizingNewton.pdf
Download
DigitizingNewton_2up.pdf
Download
DigitizingNewton_4up.pdf
``
Introduction to Physical Signal Models
'', by
Julius O. Smith III
, (From Lecture Overheads,
Music 420
).
Copyright ©
2020-06-27
by
Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),
Stanford University
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