# Module: inertial3DSpin¶

## Executive Summary¶

Module to compute the Inertial-3D spinning pointing navigation solution. This spin can be relative to an inertial frame or relative to an input reference frame message.

## Message Connection Descriptions¶

The following table lists all the module input and output messages. The module msg connection is set by the user from python. The msg type contains a link to the message structure definition, while the description provides information on what this message is used for.

Module I/O Messages

Msg Variable Name

Msg Type

Description

attRefOutMsg

attitude reference output message

attRefInMsg

(optional) attitude reference input message, if not connected then a zeroed input reference state is set

## Module Description¶

This module generates an attitude reference frame state output message where the reference frame is rotating at a constant angular velocity vector relative to the input frame $$R_0$$. If the input attitude frame message is not connected, then a zero’d input message is assumed.

The input reference frame $$R_0$$ (user defined input message or default zero’d message) contains the state information in the form $$\pmb\sigma_{R_0/N}$$, $$\pmb\omega_{R_0/N}$$ and $$\dot{\pmb\omega}_{R_0/N}$$. The constant spin vector is constant with respect to $$R_0$$ and given by $${}^{R_0}{\pmb\omega}_{R/R0}$$.

The angular velocity of the of the output reference frame $$R$$ is then given by

$\pmb \omega_{R/N} = \pmb\omega_{R/R_0} + \pmb\omega_{R_0/N}$

As the spin vector $${}^{R_0}{\pmb\omega}_{R/R0}$$ is constant with respect to $$R_0$$, then the output frame angular acceleration is

$\dot{\pmb\omega}_{R/N} = {\pmb\omega}_{R_0/N} \times {\pmb\omega}_{R/R0} + \dot{\pmb\omega}_{R_0/N}$

Finally, the output frame MRP orientation is computed using

$\dot{\pmb\sigma}_{R/N} = \frac{1}{4} [B(\pmb\sigma_{R/N})]\ {}^{R}{\pmb\omega}_{R/N}$

where

$[B(\pmb\sigma_{R/N})] = (1-\sigma_{R/N}^{2}) [I_{3\times 3}] + 2 [\tilde{\pmb\sigma}_{R/N}] + 2 \pmb\sigma_{R/N} \pmb\sigma_{R/N}^{T}$

with $$\sigma_{R/N} = |\pmb\sigma_{R/N}|$$.

## User Guide¶

The only parameter that must be set is omega_RR0_R0 representing the $$R_0$$-constant spin axis $${}^{R_0}{\pmb\omega}_{R/R0}$$.

Functions

void SelfInit_inertial3DSpin(inertial3DSpinConfig *configData, int64_t moduleID)

This method initializes the configData for this module. It checks to ensure that the inputs are sane and then creates the output message

Parameters
• configData – The configuration data associated with this module

• moduleID – The ID associated with the configData

Returns

void

void Update_inertial3DSpin(inertial3DSpinConfig *configData, uint64_t callTime, int64_t moduleID)

This method performs all the main computations of the module

Parameters
• configData – The configuration data associated with the MRP Steering attitude control

• callTime – The clock time at which the function was called (nanoseconds)

• moduleID – The ID associated with the configData

Returns

void

void Reset_inertial3DSpin(inertial3DSpinConfig *configData, uint64_t callTime, int64_t moduleID)

This method performs a complete reset of the module. Local module variables that retain time varying states between function calls are reset to their default values.

Parameters
• configData – The configuration data associated with the MRP steering control

• callTime – The clock time at which the function was called (nanoseconds)

• moduleID – The ID associated with the configData

Returns

void

void computeReference_inertial3DSpin(inertial3DSpinConfig *configData, double omega_R0N_N, double domega_R0N_N, double omega_RR0_R, double dt)
struct inertial3DSpinConfig
#include <inertial3DSpin.h>

module configuration structure definition.

Public Members

double sigma_RN

MPR of reference frame relative to inertial N frame

double omega_RR0_R0

[r/s] constant angular velocity spin vector of the spinning R frame relative to the input frame R0

uint64_t priorTime

[ns] last time the guidance module is called

AttRefMsg_C attRefOutMsg

reference attitude output message

AttRefMsg_C attRefInMsg

(optional) reference attitude input message