Maths - Euler Angles

Date: Tue, 11 Jul 2006 14:17:32 +0530
From: "Dr. Kissinger Henry"
To: martinbaker
Subject: Request

Dear martin,

your program on

https://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToMatrix/program/index.htm

was simply amazing.

I observed that same orientation occurs at two different rotation angles for heading,attitude and bank.

(ie)Structure at the orientation A(Heading=150, Attitude=0, Bank=150)  is similar to the orientation B(heading=330, Attitude=180, Bank=330).

Please explain me the funda behind this.

Is there is any formula or program available to predict the similar orientations with two different set(Heading,Attitude,Bank) of values for rotation angles.Please let me know as soon as possible.

Thanks and Regards

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From: mjb
To: "Dr. Kissinger Henry"
Subject: Re: Request
Date: Tue, 11 Jul 2006 19:24:04 +0100

Hi Kissinger Henry,

I think that there is normally a 1:1 relationship between any given
orientation and the euler angles that represent it (but I cant prove it!).

However, we have to be careful about the exceptions to this, when the euler
angles are defined as they are on the web site then:

We constrain:
heading between 0 and 360 degrees (or -180 and + 180)
attitude between 0 and 180degrees (or -90 and + 90)
bank between 0 and 360 degrees (or -180 and + 180)

There are many values which will give the singularities at:
attitude = -90 or +90

I'm not surprised that attitude of 0 or 180 degrees can give the same
orientation since they are at the extreme ends of the range for attitude.

To take a simpler but similar example, when we define a point on the earths
surface by latitude and longitude.
longitude varies from 0 to 360 degrees
latitude varies from -90 to +90 degrees
We can see that if latitude were to go above 90 degrees, we would go over the
north pole which is the same as going around the world.

Its an interesting question, would it be alright if I include it on the
website?

Martin

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Date: Wed, 12 Jul 2006 21:43:34 +0530
From: "Dr. Kissinger Henry"
To: mjb Subject:
Re: Request

Dear martin,

I will be very much happy if you are going to post this question on website too.

I am sure that there will be some formula available in this earth, to calculate the similar orientations.

I hope posting this question would be useful for many,  also we may get some

solutions too from the users.

Thanks and Regards

Kissinger Henry