Understanding Kinematics for Inertial to Body Conversion

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Discussion Overview

The discussion revolves around the conversion of kinematic parameters from an inertial frame to a body frame, specifically in the context of simulating an inertial navigation system (INS) using Simulink. Participants explore the necessary steps and equations involved in this conversion process, including the use of quaternions for rotation and the implications of working in different coordinate systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks guidance on converting initial position, velocity, and quaternion data into rotational rates and linear acceleration for a simulation.
  • Another participant emphasizes the importance of understanding quaternion rotations and suggests that there are no shortcuts to mastering the necessary concepts.
  • A participant points out that working in an inertial coordinate system is generally easier due to the presence of conservation laws and the absence of fictitious forces.
  • There is a question about whether the initial position and velocity should be transformed into inertial coordinates and the rationale behind this transformation.
  • Clarification is sought on whether the goal is to simulate what the INS measures from given coordinates and orientation or to integrate body accelerations to find inertial position and orientation.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the conversion process and the use of coordinate systems. There is no consensus on the specific steps required or the best approach to take, indicating that multiple competing views remain.

Contextual Notes

Some participants mention the need for a solid understanding of linear algebra and quaternion rotations, highlighting potential limitations in knowledge that may affect the discussion. The exact mathematical steps and assumptions involved in the conversion process remain unresolved.

Who May Find This Useful

This discussion may be useful for individuals interested in kinematics, inertial navigation systems, and the application of quaternion mathematics in simulations, particularly those working in engineering fields such as electrical or mechanical engineering.

Pikapi
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Hey Everyone,

I basically need a crash course on kinematics as I am trying to model this in simulink. I am given an intial set of position, velocity, ECI to Body Quaternion and suppose to convert into rotational rate and linear acceleration. Can anyone explain what i need to do? I tried looking it up but honestly the equations are above me. It seems that I am also suppose to convert from inertial to body but i am not sure why and how i am suppose to do this. I'm an EE and not mechanical so please bear with me, it's been a while since i worked with this.
 
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I guess I should also explain that this is to simulate an inertial navigation system.
 
If you don't understand how quaternion rotations work, you have two options. Either learn linear algebra, which will take a while, or find someone else to do the work for you. There is no shortcut for this problem.
 
Actually i do know how to work with linear algebra, but I'm confused on what steps I need to take. For example, when given an initial position and velocity, do we need to first transform them into inertial coordinates and why do we need them in inertial coordinates?
 
It's always easier to work with these things in inertial coordinate system. For one thing, you have conservation laws on your side. For another, no fictitious forces.

So what exactly do you have, in terms of running variables, and what exactly are you trying to do? Usually, INS gives you body accelerations and you integrate these to inertial position and orientation. Is that what you are trying to do, or are you trying to solve the reverse problem? Given coordinates/orientation try to simulate what INS is going to measure?
 

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