Waves On a Sphere
Waves On a Sphere
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In our eReader you can find the full English version of the book. Read Waves On a Sphere Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Waves On a Sphere
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J.
Li'-r :i e. : 11 3« Bernoulli-type Solution. We proceed now to solve (12) ^li^&^i^ ®l!=^^tt -■jt j. «;-.
- r Loo eXd'i- TC ^ Vi! ■ '. 'nei7©5aj: -» — ^•- I > K > I 9 u, ^^ !r':- 12 where ■;^(x, t) = \l/(arc cos x, t) with the initial conditions V(x, 0) = (16) /4. (x, 0) = f(arc cos x) = P(x), The Bernoulli-type representation of the solution of ( l5), (16) as an eigenf unction expansion can easily be found by using the Legendre transform 1 7L-"'(n, t) = I P^(x)X(x, t)dx where n is an integer... and '■n is small. This remark of course merely vinderlines the well known disadvantage of expressing solutions of wave motion problems as an infinite series of functions involving the time. We can expect a clearer plctvire of the wave motion if we can express \I/(o, t) as the sum of a finite number of terms. The series (19) can be siommed by applying the Laplace transform with respect to t, and sub- sequently using various identities and expansions Involving the Legendre fixnctions.
What to read after Waves On a Sphere?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Sylvester Peters to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
J.
Li'-r :i e. : 11 3« Bernoulli-type Solution. We proceed now to solve (12) ^li^&^i^ ®l!=^^tt -■jt j. «;-.
- r Loo eXd'i- TC ^ Vi! ■ '. 'nei7©5aj: -» — ^•- I > K > I 9 u, ^^ !r':- 12 where ■;^(x, t) = \l/(arc cos x, t) with the initial conditions V(x, 0) = (16) /4. (x, 0) = f(arc cos x) = P(x), The Bernoulli-type representation of the solution of ( l5), (16) as an eigenf unction expansion can easily be found by using the Legendre transform 1 7L-"'(n, t) = I P^(x)X(x, t)dx where n is an integer... and '■n is small. This remark of course merely vinderlines the well known disadvantage of expressing solutions of wave motion problems as an infinite series of functions involving the time. We can expect a clearer plctvire of the wave motion if we can express \I/(o, t) as the sum of a finite number of terms. The series (19) can be siommed by applying the Laplace transform with respect to t, and sub- sequently using various identities and expansions Involving the Legendre fixnctions.
What to read after Waves On a Sphere?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Sylvester Peters to read onlineMoreLess
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