Postcard
It’s particularly advantageous to learn specialised arts from different experts to get a wider view of the entire situation.
While in college in Malaysia, my mechanics lecturer was a Dr Gowda, an Indian national. Gowda writes his vectors in this form: r = xi + yj. The vectors are marked by underlining them with a squiggle ~. For cross products of unit vectors, this little relationship is used:
i, j, k, i...
If the two unit vectors come one after another, then the product is the third vector: i x j = k or k x i = j.
If they go backwards, then the product is negative: j x i = -k.
At Melbourne, the lecturer who handles all dynamics courses is a Dr Krodkiewski of Polish origin. He writes his vectors in this form: r = ix + jy and the vectors underlined with a squiggle. He never needed any tricks to obtain the cross products of unit vectors: everything is done in full, by expressing them as a sum of i j k and doing the cross product via the matrix determinant. While the style is tedious at times, but mechanical and not prone to errors due to brain fade. The same could be said of Krodkiewski’s approach to derivations and calculations- all the procedures are done precisely, step by step, very formal and easy to proofread.
Recently, the university pawned a Prof Pandy from Texas A&M for a position in biomechanics. He does things a bit differently. Instead of ΣF = ma, Pandy uses D’Alembert’s approach of ΣF – ma = 0. An extra vector is added into each object, the inertia force ma. The problem is then solved like in statics. For the cross product of unit vectors, he uses the right handed screw to visualise the problem. I can illustrate hand motions with text, so we’ll not talk about that. He underlines his vectors using a straight line instead of a squiggle.
Enough rubbish for today.
Just for fun, the third person to email his/her full postal address to bare_proton[at] yahoo.co.uk will get a postcard from Melbourne, Australia. Open to everyone, even if I do not know you, wherever you are. Enter "Postcard" in the subject line. [event closed]
While in college in Malaysia, my mechanics lecturer was a Dr Gowda, an Indian national. Gowda writes his vectors in this form: r = xi + yj. The vectors are marked by underlining them with a squiggle ~. For cross products of unit vectors, this little relationship is used:
i, j, k, i...
If the two unit vectors come one after another, then the product is the third vector: i x j = k or k x i = j.
If they go backwards, then the product is negative: j x i = -k.
At Melbourne, the lecturer who handles all dynamics courses is a Dr Krodkiewski of Polish origin. He writes his vectors in this form: r = ix + jy and the vectors underlined with a squiggle. He never needed any tricks to obtain the cross products of unit vectors: everything is done in full, by expressing them as a sum of i j k and doing the cross product via the matrix determinant. While the style is tedious at times, but mechanical and not prone to errors due to brain fade. The same could be said of Krodkiewski’s approach to derivations and calculations- all the procedures are done precisely, step by step, very formal and easy to proofread.
Recently, the university pawned a Prof Pandy from Texas A&M for a position in biomechanics. He does things a bit differently. Instead of ΣF = ma, Pandy uses D’Alembert’s approach of ΣF – ma = 0. An extra vector is added into each object, the inertia force ma. The problem is then solved like in statics. For the cross product of unit vectors, he uses the right handed screw to visualise the problem. I can illustrate hand motions with text, so we’ll not talk about that. He underlines his vectors using a straight line instead of a squiggle.
Enough rubbish for today.
posted by Tan Yee Wei at 8/02/2005 10:54:00 pm
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