ecce.monkey
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I have started going through Lanczos' book "The Variational Principles of Mechanics", and have got stuck on the first problem he gives at 16.9 to do with holonomic constraints
Investigate the integrability of the following differential relation:
x dz + (y2 - x2 - z) dx + (z - y2 - xy) dy = 0 (16.9)
He then states that the condition is indeed holonomic and can be replaced by the finite relation:
z = x2 - xy + y2 (16.10)
I just can't get anywhere with this problem using the holonomic condition in (16.7). I can't even see how to go backwards from 16.10 to 16.9 using 16.2. Has anyone worked through it? Given 16.10 is symmetric in x and y whereas 16.9 isn't, I wonder if it's a misprint?
Investigate the integrability of the following differential relation:
x dz + (y2 - x2 - z) dx + (z - y2 - xy) dy = 0 (16.9)
He then states that the condition is indeed holonomic and can be replaced by the finite relation:
z = x2 - xy + y2 (16.10)
I just can't get anywhere with this problem using the holonomic condition in (16.7). I can't even see how to go backwards from 16.10 to 16.9 using 16.2. Has anyone worked through it? Given 16.10 is symmetric in x and y whereas 16.9 isn't, I wonder if it's a misprint?