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Collaboration diagram for Extrapolate Pulsar Spins and Phase:
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, and "spin-ranges" 
from one SSB epoch to another. Files | |
| file | ExtrapolatePulsarSpins.h |
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| file | ExtrapolatePulsarSpins.c |
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, and "spin-ranges" from one SSB epoch to another.
and 
(where "canonical" ordering refers to 
for all k.The extrapolation is defined by the pulsar spindown-model:
![\[ f(\tau_1) = f(\tau_0) + {\stackrel{.}{f}(\tau_0) \over 1!} \,\Delta\tau + {\ddot{f}(\tau_0) \over 2!} \,\Delta\tau^2 + ... = \sum_{k=0}^s {f^{(k)}(\tau_0) \over k!}\, \Delta\tau^k\,, \]](form_218.png)
where
![\[\Delta\tau \equiv \tau_1 - \tau_0\f\,,\]](form_219.png)
and therefore generally
![\[ f^{(l)}(\tau_1) = \sum_{k=0}^{s - l} { f^{(k+l)}(\tau_0) \over k! }\, \Delta\tau^k\,. \]](form_220.png)
This expression is used to extrapolate a whole "spin-range", namely at each spindown-order 
the extrapolated range is given by
![\[ \min\left[ f^{(l)}(\tau_1) \right] = \sum_{k=0}^{s - l} {1\over k!} \min\left[ f^{(k+l)}(\tau_0) \, \Delta\tau^k \right]\,. \]](form_222.png)
![\[ \max\left[ f^{(l)}(\tau_1) \right] = \sum_{k=0}^{s - l} {1\over k!} \max\left[ f^{(k+l)}(\tau_0) \, \Delta\tau^k \right]\,. \]](form_223.png)
This ensures that the range will be correctly extrapolated even if 
, i.e. 
.
1.5.2
from one SSB epoch to another.