Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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... equations of motion describing physical systems which are linear , have a finite number of degrees of freedom , and have properties inde- pendent of time are relatively simple in nature . ( See also the last para- graph of Sec . 1.2 ...
... equations of motion describing physical systems which are linear , have a finite number of degrees of freedom , and have properties inde- pendent of time are relatively simple in nature . ( See also the last para- graph of Sec . 1.2 ...
Página 4
... equation of motion of the system may be written as mx + kx - = 0 A system which satisfies Eq . ( 1.3 ) is called a harmonic oscillator . Key это m w ko m ( 1.3 ) Figure 1.1 Figure 1.2 A somewhat more complicated system is that of two ...
... equation of motion of the system may be written as mx + kx - = 0 A system which satisfies Eq . ( 1.3 ) is called a harmonic oscillator . Key это m w ko m ( 1.3 ) Figure 1.1 Figure 1.2 A somewhat more complicated system is that of two ...
Página 5
... equations of motion be- come , in place of ( 1.4 ) , mx1 + kx1 = k 。( x2 − x1 ) + F1 ( t ) mx2 + kx2 = ko ( x1 − x2 ) + F2 ( t ) ( 1.8 ) If , in the problems indicated by ( 1.7 ) and ( 1.8 ) , the forces F , F1 , and F2 are ...
... equations of motion be- come , in place of ( 1.4 ) , mx1 + kx1 = k 。( x2 − x1 ) + F1 ( t ) mx2 + kx2 = ko ( x1 − x2 ) + F2 ( t ) ( 1.8 ) If , in the problems indicated by ( 1.7 ) and ( 1.8 ) , the forces F , F1 , and F2 are ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх