new_simple_dynamics.txt

%magnetic field and torque


mag_field = igrfmagm(lat,long,height.....)   %gives magnetic field in NED frame at the center of tether

%force

ned->IF
L_cap_IF=L_cap_BF*RM
force_mag_tether_IF = ((area/length)*dot(L_cap_IF, cross(vel_COM_IF,mag_field_IF))*cross(L*L_cap_IF,mag_field_IF)     %no frame dependant quantity so transform later?? 

%torque

force_mag_tether_BF=force_mag_tether_IF*rm
torq_mag_tether_BF= cross(L*dL_cap_BF/2,force_mag_tether_BF)



%gravitational force and torque



force_grav_sat_IF = -G*M*Ms/radius^2 
force_grav_tether_IF= -G*M*Mt/radius^2      %MASS_TETHER ?????
force_grav_sys_IF=force_grav_sat_IF+force_grav_tether_IF


force_grav_tether_BF=force_grav_IF*rm

torq_grav_BF = cross(L*dL_cap_BF/2,force_grav_tether_BF)




%dynamic equations



% w_BF is defined as angular velocity of BF wrt to an inertial frame at the posn of BF with its axis aligned to BF
%diff_eqn_1
force_mag_tether_IF + force_grav_sys_IF = (Ms+Mt)*acc_COM_IF                                             %COM is assumed at the satellite body

inertia_BF = [Ixx,-Ixy,-Ixz ; -Ixy, Iyy,-Iyz; -Ixz, -Iyz,Izz]                                     %can initialize this with constants

torq_total_BF = torq_grav_tether_BF + torq_mag_tether_BF

w_BF_dot=diff(w_BF)
                                                                               % see how to diff wrt a variable   ?????
w_rel_dot = [ dot(w_BF_dot*A,[1,0,0]) ; dot(w_BF_dot*A,[0,1,0]) ; dot(w_BF_dot*A,[0,0,1])   ]        %differentiation of scalar part of omega in IF projected along BF

%diff_Eqn_2
torq_total_BF = inertia_BF*w_rel_dot  +  cross(w_BF, inertia_BF*w_BF)       % here w_rel_dot is same as w_dot