{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 10 128 0 0 1 0 2 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 1 11 0 0 0 1 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 0 0 128 128 1 2 0 1 0 0 0 0 0 0 }{CSTYLE "2D Input" 2 19 "" 0 0 128 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "Non-proport ional" -1 256 "Courier" 1 11 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "" -1 258 "Verdana" 1 11 0 0 128 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "" -1 260 "" 0 10 0 0 0 0 0 0 0 0 0 0 3 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 0 2 0 0 0 0 0 0 }0 1 0 -1 6 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 24 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 15 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 6 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple P lot" 0 13 1 {CSTYLE "" -1 -1 "" 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "Ti mes" 1 22 0 128 128 1 0 1 0 0 0 0 0 0 0 }3 1 0 -1 14 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 128 1 0 1 0 0 0 0 0 0 0 }3 1 0 -1 8 0 0 0 0 0 0 0 261 0 }{PSTYLE "Address" 0 256 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 128 1 1 2 0 0 0 0 0 0 0 }3 1 0 -1 6 -1 0 0 0 0 0 0 263 0 }{PSTYLE "Date" 0 257 1 {CSTYLE "" -1 -1 "" 1 14 0 0 128 1 2 0 0 0 0 0 0 0 0 }3 0 0 -1 8 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Address - email" -1 258 1 {CSTYLE "" -1 -1 "Verdana" 1 10 0 0 128 1 2 0 0 0 0 0 0 0 0 }3 0 0 -1 4 -1 0 0 0 0 0 0 262 0 }{PSTYLE " " 18 259 1 {CSTYLE "" -1 -1 "" 0 1 0 128 128 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE " " 4 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 264 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 265 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 266 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 267 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 268 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 269 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 270 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 271 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }{PSTYLE "" 4 272 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 2 0 -1 0 }} {SECT 0 {PARA 259 "" 0 "Top" {TEXT -1 50 "Graphical Portraits of\nSele cted Coordinate Systems" }}{PARA 19 "" 0 "" {TEXT -1 15 "Marc A. Muris on" }}{PARA 256 "" 0 "" {TEXT -1 75 "Astronomical Applications Departm ent\nU. S. Naval Observatory\nWashington, DC" }}{PARA 258 "" 0 "" {TEXT 258 62 "murison@riemann.usno.navy.mil\nhttp://aa.usno.navy.mil/m urison/" }}{PARA 257 "" 0 "" {TEXT -1 12 "21 May, 1998" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Contents " }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 613 "This document contains simple 2D \+ and 3D plots representing certain selected coordinate systems. In eac h 3D plot are three surfaces, each a constant over one of the coordina tes. The 2D plots are two sets of coordinate curves for a given value of the third coordinate \226 that is, an intersection of a specific c oordinate surface with families of the other two coordinate surfaces. \+ The coordinate systems are a small subset of ones known by Maple; the y were chosen for my own peculiar reasons and are therefore not repres entative of anything in particular. The Maple coordinate systems are \+ listed in the help for " }{HYPERLNK 17 "coords" 2 "coords" "" }{TEXT -1 3 ". " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 " Click on a link to go directly to that section. Alternately, use the \+ bookmarks for navigation (under the View menu item)." }{MPLTEXT 1 0 0 "" }}}{PARA 260 "" 0 "" {HYPERLNK 17 "Spherical" 1 "" "Spherical" }} {PARA 261 "" 0 "" {HYPERLNK 17 "Paraboloidal" 1 "" "Paraboloidal" }} {PARA 262 "" 0 "" {HYPERLNK 17 "Oblate Spheroidal" 1 "" "Oblate Sphero idal" }}{PARA 263 "" 0 "" {HYPERLNK 17 "Inverse Oblate Spheroidal" 1 " " "Inverse Oblate Spheroidal" }}{PARA 264 "" 0 "" {HYPERLNK 17 "Prolat e Spheroidal" 1 "" "Prolate Spheroidal" }}{PARA 265 "" 0 "" {HYPERLNK 17 "Inverse Prolate Spheroidal" 1 "" "Inverse Prolate Spheroidal" }} {PARA 266 "" 0 "" {HYPERLNK 17 "Toroidal" 1 "" "Toroidal" }}{PARA 267 "" 0 "" {HYPERLNK 17 "Bipolar Cylindrical" 1 "" "Bipolar Cylindrical" }}{PARA 268 "" 0 "" {HYPERLNK 17 "Bispherical" 1 "" "Bispherical" }} {PARA 269 "" 0 "" {HYPERLNK 17 "Tangent Spheroidal" 1 "" "Tangent Sphe roidal" }}{PARA 270 "" 0 "" {HYPERLNK 17 "Cardioidal" 1 "" "Cardioidal " }}{PARA 271 "" 0 "" {HYPERLNK 17 "6-Sphere" 1 "" "6-Sphere" }}{PARA 272 "" 0 "" {HYPERLNK 17 "Maxwell Cylindrical" 1 "" "Maxwell Cylindric al" }}}{PARA 0 "" 0 "" {MPLTEXT 1 0 0 "" }}{SECT 1 {PARA 3 "" 0 "Spher ical" {TEXT -1 9 "Spherical" }}{EXCHG {PARA 0 "" 0 "" {TEXT 23 73 " sp herical:\n x = u*cos(v)*sin(w)\n y = u*sin(v)*sin(w)\n z = u*cos (w)" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 19 1 "xyz := fn([u*cos(v)*sin( w), u*sin(v)*sin(w), u*cos(w)],u,v,w):" "6#>%$xyzG-%#fnG6&7%*(%\"uG\" \"\"-%$cosG6#%\"vGF+-%$sinG6#%\"wGF+*(F*F+-F16#F/F+-F16#F3F+*&F*F+-F-6 #F3F+F*F/F3" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 19 1 "coordplot3D(xyz( u,v,w),u[0] = .8,v[0] = 0,w[0] = evalf(Pi/3),u = 0 .. 1,v = -Pi .. Pi, w = 0 .. Pi,orientation = [-145, 70],view = [0 .. 1, -1 .. 1, 0 .. 1], title = \"Spherical Coordinates\");" "6#-%,coordplot3DG6,-%$xyzG6%%\"u G%\"vG%\"wG/&F)6#\"\"!$\"\")!\"\"/&F*6#F/F//&F+6#F/-%&evalfG6#*&%#PiG \"\"\"\"\"$!\"\"/F);F/\"\"\"/F*;,$F=F@F=/F+;F/F=/%,orientationG7$,$\"$ X\"F@\"#q/%%viewG7%;F/\"\"\";,$\"\"\"F@\"\"\";F/\"\"\"/%&titleGQ6Spher ical~Coordinates6\"" }}{PARA 13 "" 1 "" {GLPLOT3D 653 548 548 {PLOTDATA 3 "6/-%%MESHG6%W*gcu\"?\"?\"$8000000000000000800000000000000 03FE999999999999ABFB6248CE690AE60BCB42361780121D43FE9732EB95E7840BFC60 35234200EF7BCC40528E06F52A03FE9006166BCD476BFD0592625E63C57BCCDBC8A8A1 27FF73FE8428A31D16DDEBFD57F9207D462BABCD38D561711D3FF3FE73BE2E29D30A8B FDA6577AF2E2E30BCD801B81091470D3FE5EF7FCAE5F513BFDEFC23B48726E4BCDC2E0 C7CD646023FE46146882D8518BFE19AE83C8675CBBCE002E674849B6A3FE295E2517C3 E77BFE382E7BE1A3FB4BCE1BEB85DF2FD2E3FE092B5F41A0853BFE53057B5D593AFBCE 34547E9C817CC3FDCBB975288AFA4BFE69E2F3DA6DAD4BCE49200E0CE305C3FD7FB85E 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Pi,orientation = [-145, \+ 60],view = [0 .. .8, -.8 .. .8, -.5 .. .5],title = \"Paraboloidal Coor dinates\");" "6#-%,coordplot3DG6,-%$xyzG6%%\"uG%\"vG%\"wG/&F)6#\"\"!$ \"\"(!\"\"/&F*6#F/$\"\"(!\"\"/&F+6#F/F//F);F/\"\"\"/F*;F/\"\"\"/F+;,$% #PiG!\"\"FE/%,orientationG7$,$\"$X\"FF\"#g/%%viewG7%;F/$\"\")!\"\";,$$ \"\")!\"\"FF$\"\")!\"\";,$$\"\"&!\"\"FF$\"\"&!\"\"/%&titleGQ9Paraboloi dal~Coordinates6\"" }}{PARA 13 "" 1 "" {GLPLOT3D 653 548 548 {PLOTDATA 3 "6/-%%MESHG6%W*gcu\"?\"?\"$8000000000000000800000000000000 03FCF5C28F5C28F5C800000000000000080000000000000003FCF5C28F5C28F5C80000 0000000000080000000000000003FCF5C28F5C28F5C800000000000000080000000000 000003FCF5C28F5C28F5C800000000000000080000000000000003FCF5C28F5C28F5C8 00000000000000080000000000000003FCF5C28F5C28F5C80000000000000008000000 0000000003FCF5C28F5C28F5C800000000000000080000000000000003FCF5C28F5C28 F5C000000000000000080000000000000003FCF5C28F5C28F5C0000000000000000800 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