I have the following differential expression:
f =
{h''[t] + 0.25 alpha''[t] + 0.1 h'[t] + 0.2 h[t] + 0.1 q alpha[t],
0.25 h''[t] + 0.5 alpha''[t] + 0.1 alpha'[t] + (k0 - 0.04 q) alpha[t] +
e2 (alpha[t])^3}
Where k0, e2
are simple constants, and q
is a parameter. I would like to change my time variable t
, with a new variable:
tau -> t omega /n
Where omega
and n
are to be considered as constants. In order to obtain a differential equation of the following form:
$\qquad f(\omega^2 x'',\, \omega\, x',\, x, n\, \tau,\, q)=0$
If I try replacing in the simple manner,
f /. t -> (n tau)/omega
I get in turn:
{0.1 q alpha[(n tau)/omega] + 0.2 h[(n tau)/omega] + 0.1 Derivative[1][h][(n tau)/omega] + 0.25 (alpha^′′)[(n tau)/omega] + (h^′′)[(n tau)/omega], (k0 - 0.04 q) alpha[(n tau)/omega] + e2 alpha[(n tau)/omega]^3 + 0.1 Derivative[1][alpha][(n tau)/omega] + 0.5 (alpha^′′)[(n tau)/omega] + 0.25 (h^′′)[(n tau)/omega]}
Yet in this way I'm afraid Mathematica can't tell omega
and n
are constants.
I found that it is possible to declare "constants" in Dt
. Yet I would have to apply it before introducing the change of variables.
Update
Following Kuba's comment I tried implementing the following instruction:
dChange[f, tau == t omega/n, t, tau, {h[t], alpha[t]}]
having defined dChange
from this question.
My problem is solved, thanks to Kuba.
dChange[ f, tau == t omega/n, t, tau, { h[t], alpha[t] } ]
from change of variables in differential expressions $\endgroup$f
given at the beginning of your Q. I get the error on the code following your "I get in turn," but that code has been miscopied. (You may also find this this meta Q&A helpful for copying the input form of code.) $\endgroup$