\contentsline {chapter}{\numberline {1}DEFINITIONS AND MATHEMATICAL FORMULAS}{5}
\contentsline {section}{\numberline {1.1}DESCRIPTION OF COORDINATE SYSTEMS}{6}
\contentsline {subsection}{\numberline {1.1.1}Geocentric Equatorial Inertial System (GEI)}{6}
\contentsline {subsection}{\numberline {1.1.2}Geographic System (GEO)}{7}
\contentsline {subsection}{\numberline {1.1.3}Geomagnetic system (MAG)}{7}
\contentsline {subsection}{\numberline {1.1.4}Geocentric Solar Ecliptic system (GSE)}{8}
\contentsline {subsection}{\numberline {1.1.5}Geocentric Solar Equatorial system (GSEQ)}{8}
\contentsline {subsection}{\numberline {1.1.6}Geocentric Solar Magnetospheric system (GSM)}{9}
\contentsline {subsection}{\numberline {1.1.7}Solar Magnetic system (SM)}{9}
\contentsline {subsection}{\numberline {1.1.8}Dipole Meridian system (DM)}{10}
\contentsline {subsection}{\numberline {1.1.9}Vertical Dusk Horizontal system (VDH)}{10}
\contentsline {subsection}{\numberline {1.1.10}Spin Reference system (SR)}{11}
\contentsline {subsection}{\numberline {1.1.11}Spin Reference 2 system (SR2)}{11}
\contentsline {subsection}{\numberline {1.1.12}Magnetic Field Aligned system (MFA)}{12}
\contentsline {section}{\numberline {1.2}DIAGRAM OF TRANSFORMATIONS}{13}
\contentsline {subsection}{\numberline {1.2.1}General remarks}{13}
\contentsline {subsection}{\numberline {1.2.2}Schematic diagram of transformations}{13}
\contentsline {subsection}{\numberline {1.2.3}List of transformations}{14}
\contentsline {section}{\numberline {1.3}MATHEMATICAL EXPRESSIONS OF TRANSFORMATION MATRIX}{15}
\contentsline {subsection}{\numberline {1.3.1}General remarks on transformation matrix}{15}
\contentsline {subsection}{\numberline {1.3.2}GEI to GEO transformation}{16}
\contentsline {subsection}{\numberline {1.3.3}GEI to MAG transformation}{17}
\contentsline {subsection}{\numberline {1.3.4}GEI to SM transformation}{19}
\contentsline {subsection}{\numberline {1.3.5}GEI to GSM transformation}{21}
\contentsline {subsection}{\numberline {1.3.6}GEI to GSE transformation}{23}
\contentsline {subsection}{\numberline {1.3.7}GEI to GSEQ transformation}{24}
\contentsline {subsection}{\numberline {1.3.8}GSE to GSEQ transformation}{25}
\contentsline {subsection}{\numberline {1.3.9}GSE to GSM transformation}{27}
\contentsline {paragraph}{}{28}
\contentsline {paragraph}{}{29}
\contentsline {subsection}{\numberline {1.3.10}GSM to SM transformation}{31}
\contentsline {subsection}{\numberline {1.3.11}SM to MAG transformation}{33}
\contentsline {paragraph}{}{35}
\contentsline {paragraph}{}{36}
\contentsline {subsection}{\numberline {1.3.12}GEO to MAG transformation}{37}
\contentsline {subsection}{\numberline {1.3.13}GEO to SM transformation}{38}
\contentsline {subsection}{\numberline {1.3.14}GEO to GSM transformation}{40}
\contentsline {subsection}{\numberline {1.3.15}GEO to GSE transformation}{42}
\contentsline {subsection}{\numberline {1.3.16}GEO to GSEQ transformation}{44}
\contentsline {subsection}{\numberline {1.3.17}GEO to DM transformation}{46}
\contentsline {subsection}{\numberline {1.3.18}GEO to VDH transformation}{48}
\contentsline {subsection}{\numberline {1.3.19}SR2 to GSE transformation}{50}
\contentsline {subsection}{\numberline {1.3.20}SR2 to MFA transformation}{52}
\contentsline {paragraph}{}{54}
\contentsline {paragraph}{}{54}
\contentsline {paragraph}{}{54}
\contentsline {subsection}{\numberline {1.3.21}SR to SR2 transformation}{56}
\contentsline {section}{\numberline {1.4}CALENDAR CONVERSIONS}{57}
\contentsline {subsection}{\numberline {1.4.1}General remarks}{57}
\contentsline {subsection}{\numberline {1.4.2}List of calendar conversions and definitions}{57}
\contentsline {subsubsection}{$\bullet $ compute if a given year is or not a leap year (coleapy)}{57}
\contentsline {subsubsection}{ $\bullet $ compute day of the year from given date (cdoyear)}{57}
\contentsline {subsubsection}{$\bullet $ compute date from given day of the year and year (cdatdoy)}{57}
\contentsline {subsubsection}{$\bullet $ compute Julian day 1950 from given date (cjd1950)}{57}
\contentsline {subsubsection}{$\bullet $ compute Julian day 2000 from given date (cjd2000)}{58}
\contentsline {subsubsection}{$\bullet $ compute date from given 1950 Julian day (cdatj50)}{58}
\contentsline {subsubsection}{$\bullet $ compute date from given 2000 Julian day (cdatj00)}{58}
\contentsline {subsubsection}{$\bullet $ compute decimal hour from given hour, minute and second (chouday)}{58}
\contentsline {subsubsection}{$\bullet $ compute hour, minute and second from given decimal hour (ctimhou)}{58}
\contentsline {subsubsection}{$\bullet $ compute millisec. of the day from jour, hour, min,sec.,ms. (cmilday)}{58}
\contentsline {subsubsection}{$\bullet $ compute time from millisec. of the day (ctimmil)}{58}
\contentsline {subsubsection}{$\bullet $ compute week number in a year from a given date (cweedoy)}{58}
\contentsline {subsubsection}{$\bullet $ compute day of the week for a given date (doweek)}{58}
\contentsline {subsubsection}{$\bullet $ compute date from the week number of the year (cdatweek)}{59}
\contentsline {subsubsection}{$\bullet $ compute number of day in a month (cnbdmon)}{59}
\contentsline {subsubsection}{$\bullet $ compute US day name (cusdayn)}{59}
\contentsline {subsubsection}{$\bullet $ compute french day name (cfrdayn)}{59}
\contentsline {subsubsection}{$\bullet $ compute US month name (cusmonn)}{59}
\contentsline {subsubsection}{$\bullet $ compute french month name (cfrmonn)}{59}
\contentsline {chapter}{\numberline {2}USER'S MANUAL}{60}
\contentsline {section}{\numberline {2.1}DESCRIPTION OF AVAILABLE MODULES}{61}
\contentsline {subsection}{\numberline {2.1.1}General remarks}{61}
\contentsline {paragraph}{ a) \emph {"Basic computation subroutines"}}{61}
\contentsline {paragraph}{b) \emph {"Calendar subroutines"}}{61}
\contentsline {paragraph}{c) \emph {"Give subroutines"}}{61}
\contentsline {paragraph}{d) \emph {"Read and check subroutines"}}{61}
\contentsline {paragraph}{e) \emph {"Transformations subroutines"}}{61}
\contentsline {subsection}{\numberline {2.1.2}Description of "Basic Computation" subroutines}{62}
\contentsline {paragraph}{ctimpar}{62}
\contentsline {paragraph}{ctimpa2}{63}
\contentsline {paragraph}{ctimpa3}{63}
\contentsline {paragraph}{cdipdir}{63}
\contentsline {paragraph}{csundir}{63}
\contentsline {paragraph}{cangrat}{64}
\contentsline {paragraph}{csunset}{64}
\contentsline {subsection}{\numberline {2.1.3}Description of "Calendar" subroutines}{65}
\contentsline {paragraph}{cdatdoy}{65}
\contentsline {paragraph}{cdatj00}{65}
\contentsline {paragraph}{cdatj50}{65}
\contentsline {paragraph}{cdatwee}{65}
\contentsline {paragraph}{cdoweek}{65}
\contentsline {paragraph}{cdoyear}{66}
\contentsline {paragraph}{cfrdayn}{66}
\contentsline {paragraph}{cfrmonn}{66}
\contentsline {paragraph}{chouday}{66}
\contentsline {paragraph}{cjd1950}{66}
\contentsline {paragraph}{cjd2000}{66}
\contentsline {paragraph}{cmilday}{67}
\contentsline {paragraph}{cnbdmon}{67}
\contentsline {paragraph}{coleapy}{67}
\contentsline {paragraph}{ctimhou}{67}
\contentsline {paragraph}{ctimmil}{67}
\contentsline {paragraph}{cusdayn}{67}
\contentsline {paragraph}{cusmonn}{68}
\contentsline {paragraph}{cweedoy}{68}
\contentsline {subsection}{\numberline {2.1.4}Description of "Give" subroutines}{69}
\contentsline {paragraph}{gdipdir}{69}
\contentsline {paragraph}{gdiptan}{69}
\contentsline {paragraph}{gecldir}{69}
\contentsline {paragraph}{gsrodir}{69}
\contentsline {paragraph}{gsundir}{69}
\contentsline {paragraph}{gsunpar}{70}
\contentsline {paragraph}{gvernum}{70}
\contentsline {subsection}{\numberline {2.1.5}Description of "Read and check" subroutines}{71}
\contentsline {paragraph}{recoor}{71}
\contentsline {paragraph}{recys}{71}
\contentsline {paragraph}{redate}{71}
\contentsline {paragraph}{retime}{71}
\contentsline {subsection}{\numberline {2.1.6}Description of "Transformations" subroutines}{71}
\contentsline {paragraph}{tcarsph}{72}
\contentsline {paragraph}{tsphcar}{72}
\contentsline {paragraph}{tgeigeo}{72}
\contentsline {paragraph}{tgeogei}{72}
\contentsline {paragraph}{tgeimag}{72}
\contentsline {paragraph}{tmaggei}{72}
\contentsline {paragraph}{tgeisma}{73}
\contentsline {paragraph}{tsmagei}{73}
\contentsline {paragraph}{tgeigsm}{73}
\contentsline {paragraph}{tgsmgei}{73}
\contentsline {paragraph}{tgeigse}{73}
\contentsline {paragraph}{tgsegei}{73}
\contentsline {paragraph}{tgeigsq}{74}
\contentsline {paragraph}{tgsqgei}{74}
\contentsline {paragraph}{tgsegsq}{74}
\contentsline {paragraph}{tgsqgse}{74}
\contentsline {paragraph}{tgsegsm}{74}
\contentsline {paragraph}{tgsmgse}{74}
\contentsline {paragraph}{tgsmsma}{75}
\contentsline {paragraph}{tsmagsm}{75}
\contentsline {paragraph}{tgsmgsq}{75}
\contentsline {paragraph}{tgsqgsm}{75}
\contentsline {paragraph}{tgsmmag}{75}
\contentsline {paragraph}{tmaggsm}{75}
\contentsline {paragraph}{tsmamag}{76}
\contentsline {paragraph}{tmagsma}{76}
\contentsline {paragraph}{tgeomag}{76}
\contentsline {paragraph}{tmaggeo}{76}
\contentsline {paragraph}{tgeosma}{76}
\contentsline {paragraph}{tsmageo}{76}
\contentsline {paragraph}{tgeogsm}{77}
\contentsline {paragraph}{tgsmgeo}{77}
\contentsline {paragraph}{tgeogse}{77}
\contentsline {paragraph}{tgsegeo}{77}
\contentsline {paragraph}{tgeogsq}{77}
\contentsline {paragraph}{tgsqgeo}{77}
\contentsline {paragraph}{tgeodme}{78}
\contentsline {paragraph}{tdmegeo}{78}
\contentsline {paragraph}{tgeovdh}{78}
\contentsline {paragraph}{tvdhgeo}{78}
\contentsline {paragraph}{tgsesr2}{79}
\contentsline {paragraph}{tsr2gse}{80}
\contentsline {paragraph}{tsr2mfa}{80}
\contentsline {paragraph}{tsr2sre}{80}
\contentsline {paragraph}{tsresr2}{81}
\contentsline {subsection}{\numberline {2.1.7}Description of "print information" subroutines}{82}
\contentsline {section}{\numberline {2.2}DIRECTIONS FOR USE}{83}
\contentsline {subsection}{\numberline {2.2.1}Package delivered for installation}{83}
\contentsline {subsection}{\numberline {2.2.2}Make the rocotlib.o object file}{85}
\contentsline {subsection}{\numberline {2.2.3} Example of Fortran user program}{86}
\contentsline {subsection}{\numberline {2.2.4} Output of "print information" subroutine}{89}
\contentsline {subsection}{\numberline {2.2.5} Check program }{90}
