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Engineers need your help.

E

eigen

Diamond Member
I am trying to show that Legendre's Equation ( along with Bessels Equation, Hermite equation,Laguree Equations, some different forms of the wave equation.....)can be written in the form of the Sturn-Liouville.Unfortunately I am lost....


i think this page http://www.rh.edu/~ernesto/C_S2000/mes/Notes/mes11.html

may be showing me what I need but the notation is foreign.

This is Homework so I am just looking for that little hint.
 
Haha... I had to do this last semester. Too many polynomials if you ask me. 😛

From your link, the very first equation is the definition of the SL-BVP if I remember correctly. Thus, all you need to do is show in which cases the Bessel/Legendre/etc equation can be put in this form. The key for Bessel is that it occurs in cases of axisymmetry, particularly when you have cylindrical coordinates. Legendre typically occurs when you use spherical coordinates. I can't remember when Hermite and Laguere come up, as I never actually needed them to solve any real problems. The geometry arises in the laplacian term (del^2*phi), and for cylindrical would be 1/r*d/dr(r*dphi/dr) to get the Bessel equation. For spherical, 1/r^2*d/dr(r^2*dphi/dr). Hope that helps.
 
Originally posted by: CycloWizard
Haha... I had to do this last semester. Too many polynomials if you ask me. 😛

From your link, the very first equation is the definition of the SL-BVP if I remember correctly. Thus, all you need to do is show in which cases the Bessel/Legendre/etc equation can be put in this form. The key for Bessel is that it occurs in cases of axisymmetry, particularly when you have cylindrical coordinates. Legendre typically occurs when you use spherical coordinates. I can't remember when Hermite and Laguere come up, as I never actually needed them to solve any real problems. The geometry arises in the laplacian term (del^2*phi), and for cylindrical would be 1/r*d/dr(r*dphi/dr) to get the Bessel equation. For spherical, 1/r^2*d/dr(r^2*dphi/dr). Hope that helps.
Click to expand...

Thanks for your help. I am just gonna go ask my prof,

 
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