Paolo De Leva

03-23-2001, 12:47 AM

Dear subscribers,

recently, I have been discussing with some colleagues about the reason

why we call "orientation/attitude matrix of reference frame B

relative to A" the rotation matrix R used to transform any vector V from B

to A, using the following formula:

V(in A) = R * V(in B)

We were neither concerned about the obvious order of the nine unit

vector components (or direction cosines) contained in the rotation matrix

performing the above operation, nor about the many different symbols used in

the literature to indicate the reference frames and the rotation matrix. The

problem was just about terminology. Here's the complete question:

Why do most authors call the above matrix "the orientation/attitude

matrix of

reference frame B relative to A", rather than "the orientation/attitude

matrix of reference frame A relative to B"?

Some of you might think that the answer is easy, and indeed it is. Yet,

here's the names of those who didn't know the answer, initially: Paolo de

Leva, Ton van den Bogert, Aurelio Cappozzo, Jesus Dapena. Is that enough for

guessing that many subscribers will be interested in reading the end of this

e-mail message?

The answer was quickly found by Jesus Dapena. It's so simple and elegant

that I can summarize it in a few words:

1) a rotation of the reference system has the same effect, on the components

of a vector V, as a rotation of that vector IN THE OPPOSITE DIRECTION!!!!

2) If the orientation of frame B relative to A is +30°, to transform a

vector from A to B you need to rotate it by -30°, which is the orientation

of A relative to B.

With kind regards,

Paolo de LEVA

University Institute of Motor Sciences

Sport Biomechanics

P. Lauro De Bosis, 6

00194 ROME - ITALY

Telephone: (39) 06.367.33.522

FAX/AM: (39) 06.367.33.517

FAX: (39) 06.36.00.31.99

Home:

Tel./FAX/AM: (39) 06.336.10.218

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recently, I have been discussing with some colleagues about the reason

why we call "orientation/attitude matrix of reference frame B

relative to A" the rotation matrix R used to transform any vector V from B

to A, using the following formula:

V(in A) = R * V(in B)

We were neither concerned about the obvious order of the nine unit

vector components (or direction cosines) contained in the rotation matrix

performing the above operation, nor about the many different symbols used in

the literature to indicate the reference frames and the rotation matrix. The

problem was just about terminology. Here's the complete question:

Why do most authors call the above matrix "the orientation/attitude

matrix of

reference frame B relative to A", rather than "the orientation/attitude

matrix of reference frame A relative to B"?

Some of you might think that the answer is easy, and indeed it is. Yet,

here's the names of those who didn't know the answer, initially: Paolo de

Leva, Ton van den Bogert, Aurelio Cappozzo, Jesus Dapena. Is that enough for

guessing that many subscribers will be interested in reading the end of this

e-mail message?

The answer was quickly found by Jesus Dapena. It's so simple and elegant

that I can summarize it in a few words:

1) a rotation of the reference system has the same effect, on the components

of a vector V, as a rotation of that vector IN THE OPPOSITE DIRECTION!!!!

2) If the orientation of frame B relative to A is +30°, to transform a

vector from A to B you need to rotate it by -30°, which is the orientation

of A relative to B.

With kind regards,

Paolo de LEVA

University Institute of Motor Sciences

Sport Biomechanics

P. Lauro De Bosis, 6

00194 ROME - ITALY

Telephone: (39) 06.367.33.522

FAX/AM: (39) 06.367.33.517

FAX: (39) 06.36.00.31.99

Home:

Tel./FAX/AM: (39) 06.336.10.218

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------