Let us assume a simple rotation motion, when angular acceleration az somewhat depends on angle Phi[t] and set as linear interpolation function in range of 0..360 degrees. To not come out from interpolation range let angle Phi to be truncated to proper range by Mod[Phi][t], 360]:
az = Interpolation[{{0., 1.}, {90., 4}, {180., 7.}, {270., 4.}, {360.,
1.}}, InterpolationOrder -> 1];
{\[Omega]s, \[CurlyPhi]s} = NDSolveValue[{
\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\ \(\[Omega][
t]\)\) == (az[Mod[\[CurlyPhi][t], 360]] + 10000),
\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\ \(\[CurlyPhi][
t]\)\) == \[Omega][t],
\[CurlyPhi][0] == 359, \[Omega][0] ==
390 }, {\[Omega], \[CurlyPhi]}, {t, 0, 0.0029}]
Let run it, and we get
InterpolatingFunction::dmval: Input value {360.052} lies outside the range of data in the interpolating function. Extrapolation will be used.
This is quite weird result - we have truncate phi by 360 and got 360.0520876770316`
Adding
EvaluationMonitor :>
Print[t, " ", \[CurlyPhi][t], " ", Mod[\[CurlyPhi][t], 360]]
Gives list like
...
0.00203059 359.813 359.813
0.00232059 359.932 359.932
InterpolatingFunction::dmval: Input value {360.052} lies outside the range of data in the interpolating function. Extrapolation will be used.
0.0026103 360.052 0.0520877
0.00248493 360. 360.
0.00248493 360. 0.
0.00248493 360. 0.
0.00248493 360. 2.19102*10^-6
Mod[] works fine in the EvaluationMonitor, but fails in main NDSolve loop.
Can anyone tell the reason of such behavior and how to fix it?
