Re: Quaternions vs. Euler Angles

Gordan Sikic wrote: 
Hello,


How much of an error should I expect to see between the two models?


I have made couple of (real time) simulations and did not have difficulties using quats instead of Euler angles. One was simulation of FAGOT antitank missile, with "fly" time cca 10-12 s, integration period 2ms.

The other was simulation of MiG-21 aircraft, with "fly" time up to 40-50 minutes.

You should be aware that using quaternions, you are no more dealing with ODE's (ordinary differential equations) but DAE's (differential algebric equations). Basically, you use 4 parameters to represent 3 mutually independent variables, meaning that you need to involve algebric constraints( i.e. use the fact that sum of the squares should be equal to unity).

bast regards,
Gordan


Right. I renormalize the quaternion every iteration.

I've done hand calculations so I know that I implemented the appropriate equations; I'm pretty sure the error is coming from the different calculations (IE: Quaternions involve only multiplication between the quaternion components and the rotation rates, whereas Euler angles involve trig functions).

So you are saying in these simulations you wrote, your answers were identical to 6 significant figures?

thanks,
Phil

.

Relevant Pages

  • Re: Defining Rotations Limits using Quaternions In 3d Space
    ... the rotation that occurs between ones upper and lower arm at the elbow ... using euler angles it may be achieved using 3 such angles. ... I am looking to achieve this using one or more quaternions. ... The example for the human arm is a difficult one: ...
    (comp.graphics.algorithms)
  • Re: Euler angles and tweening/interpolation
    ... My engine has nodes that contain the spatial information. ... Euler angles are more meaningful to someone using the node. ... > I don't have any special reference, ... I did a bunch of reading on quaternions. ...
    (microsoft.public.win32.programmer.directx.managed)
  • Re: Quaternions -
    ... If I read well then you address two separate subjects: the mathematical problem of changing from quaternions to Euler angles; the simulation of the actual control of an aircraft. ... To be specific, around 1993, 1994 I discovered a way to reduce the gimbal lock singularities in Euler angles for aircraft attitudes to just one at a time. ...
    (sci.math)
  • Re: about Euler Quaternion Conversion Software
    ... This free utility provides GUI interface to convert Euler angles to ... Quaternions around X,Y and Z axis and performs ... conjugate, addition, subtraction, multiplication, great circle ...
    (sci.math)
  • Re: Averaging quaternions
    ... recommended to interpret the camera orientation (and position ... relative merits of quaternions versus matrices, euler angles, etc., seems ... utility of Matrices, Euler Angles, and Quaternions. ...
    (comp.graphics.algorithms)