The file RMAN99_RECOMPUTED contains the periodic terms of the recomputation of the rigid Mars nutation series of RMAN99 (Roosbeek 1999).
Computational procedure explained in (Baland et al. 2020)

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Truncation criterion: prograde and/or retrograde amplitude larger than 0.025 mas. 
Solution computed with HD=0.00535464. The solution can be rescaled to any value of HD.

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Columns signification:

- j is the item number.
- Ma, Ju, Sa, Te, Ve are the mean longitudes of Mars, Jupiter, Saturn, the Earth and of Venus.
- NPh and NDe are the mean longitudes of the nodes of Phobos and Deimos, respectively.
- Periods are given in Earth solar days.
- psiC and psiS (mas) are the cosine and sine amplitudes of the nutation in longitude of the angular momentum axis.
- epsC and epsS (mas) are the cosine and sine amplitudes of the nutation in obliquity of the angular momentum axis.
- P and R (mas) are the prograde and retrograde amplitudes of the nutation of the angular momentum axis.
- pi and rho (deg) are the phases to be added to the phase of the prograde and retrograde terms, respectively.
- alphaC and alphaS (mas) are the cosine and sine amplitudes of the nutation in right ascension of the angular momentum axis.
- deltaC and deltaS (mas) are the cosine and sine amplitudes of the nutation in declination of the angular momentum axis.

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The rotation axis can be assimilated to the angular momentum axis.
The figure axis CANNOT be assimilated to the angular momentum axis.

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The values of the arguments are 
(Bretagnon and Francou 1988 : VSOP87)
(Chapront-Touzé 1990 : ESAPHO and ESADE):

Sa = 0.87401675650 +   213.2990954380 T
Ju = 0.59954649739 +   529.6909650946 T
Ma = 6.20347611291 +  3340.6124266998 T
Te = 1.75347045953 +  6283.0758499914 T
Ve = 3.17614669689 + 10213.2855462110 T
NPh= 2.19694890391 -  2779.5760599403 T
NDe= 0.19542626168 -   114.7548090403 T

where T is the dynamical time measured in thousand of years since J2000.0 

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The waves in the time domain are obtained the following way:

Delta psi = psiC Cos(varphi) + psiS Sin(varphi)
Delta eps = epsC Cos(varphi) + epsS Sin(varphi)
Delta alpha = alphaC Cos(varphi) + alphaS Sin(varphi)
Delta delta = deltaC Cos(varphi) + deltaS Sin(varphi)

with varphi = f t + varphi0, a linear combination of the arguments Sa, Ju, Ma, Te, Ve, NPh, and NDe.
f is positive.

delta x   = P Cos(f t + pi) + R Cos (-f t - rho)
delta y   = P Sin(f t + pi) + R Sin (-f t - rho)

Times series can be found in the file rman99_recomputed_TimesSeries.dat

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The J2000 epoch values are (in degrees)

psi0   = 35.496817571
eps0   = 25.192028020
alpha0 = 317.681
delta0 = 52.886

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The secular variations rates the solution are

-7578.132 mas/year in longitude for the Solar torque
   -0.232 mas/year in longitude for Phobos torque
   -0.251 mas/year in longitude for Deimos torque

-0.002 mas/year in obliquity for the Solar torque
 0.000 mas/year in obliquity for Phobos torque
 0.000 mas/year in obliquity for Deimos torque

-3894.186 mas/year in right ascension for all torques
-2210.160 mas/year in declination for all torques


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Any comments or request could be send to Baland Rose-Marie at the following e-mail address:
Rose-Marie.Baland@oma.be

Last revision: 09/01/20.