Simulation is a great way to learn about gravity. So is dancing.
This is a simple physics engine for simulating a particle in a central force field. The code is in the comments section. Here is an example of what you can do with it.Thursday, March 20, 2008
Gravity Fields
To use the force you must learn the force. Gravity is Newton's force.
Simulation is a great way to learn about gravity. So is dancing.
This is a simple physics engine for simulating a particle in a central force field. The code is in the comments section. Here is an example of what you can do with it.
Simulation is a great way to learn about gravity. So is dancing.This is a simple physics engine for simulating a particle in a central force field. The code is in the comments section. Here is an example of what you can do with it.
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max v2;
#N vpatcher 251 72 1326 670;
#P origin -25 0;
#P window setfont "Sans Serif" 20.;
#P comment 635 404 122 196628 SPACEBAR TOGGLES TRAILS;
#P window setfont "Sans Serif" 9.;
#P window linecount 1;
#P message 9 117 31 196617 0.01;
#P flonum 10 146 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#N vpatcher 340 160 940 560;
#P origin 0 -6;
#P window setfont "Sans Serif" 9.;
#P window linecount 0;
#P newex 533 152 43 196617 s space;
#P newex 190 94 54 196617 pack 1. 2.;
#P newex 259 51 27 196617 f;
#P window linecount 1;
#P newex 190 71 50 196617 poltocar;
#B color 5;
#P window linecount 0;
#P newex 211 48 29 196617 t b f;
#P newex 174 25 47 196617 cartopol;
#P inlet 279 -3 15 0;
#P newex 472 123 98 196617 sel 30 31 28 29 32;
#P number 426 123 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 447 85 40 196617 key;
#P outlet 211 346 15 0;
#P window linecount 1;
#P message 50 171 132 196617 0.003849 -0.00923;
#P newex 50 149 62 196617 prepend set;
#P newex 283 126 61 196617 vexpr -$f1;
#P message 284 169 118 196617 -0.003849 0.00923;
#P newex 284 147 62 196617 prepend set;
#P message 224 258 118 196617 -0.00923 -0.003849;
#P newex 221 243 62 196617 prepend set;
#P message 179 307 118 196617 0.00923 0.003849;
#P newex 152 282 62 196617 prepend set;
#P flonum 276 27 35 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 221 222 61 196617 vexpr -$f1;
#P newex 179 192 54 196617 pack 1. 2.;
#P newex 196 132 50 196617 expr $f1;
#P newex 179 156 55 196617 expr -$f2;
#P newex 167 123 27 196617 t l l;
#P newex 174 3 85 196617 vexpr ($f1-$f2);
#P newex 212 -25 27 196617 t l l;
#P inlet 212 -45 15 0;
#P inlet 174 -17 15 0;
#P connect 28 0 17 0;
#P connect 17 0 18 0;
#P connect 22 0 18 0;
#P connect 7 0 10 0;
#P connect 28 0 4 0;
#P fasten 2 1 3 0 234 1 179 1;
#P connect 0 0 3 0;
#P connect 3 0 24 0;
#P connect 4 0 5 0;
#P connect 5 0 7 0;
#P connect 10 0 11 0;
#P connect 22 3 11 0;
#P connect 27 0 26 0;
#P connect 26 0 28 0;
#P connect 4 1 6 0;
#P connect 24 1 25 0;
#P connect 15 0 19 0;
#P connect 13 0 19 0;
#P connect 11 0 19 0;
#P connect 18 0 19 0;
#P connect 1 0 2 0;
#P fasten 7 0 8 0 184 213 226 213;
#P connect 8 0 12 0;
#P fasten 6 0 7 1 201 180 228 180;
#P connect 12 0 13 0;
#P connect 22 2 13 0;
#P connect 25 1 26 1;
#P connect 26 1 28 1;
#P fasten 2 0 3 1 217 -4 254 -4;
#P connect 25 0 27 0;
#P connect 23 0 9 0;
#P connect 9 0 27 1;
#P connect 28 0 16 0;
#P connect 16 0 14 0;
#P connect 14 0 15 0;
#P connect 22 1 15 0;
#P connect 20 0 21 0;
#P connect 20 0 22 0;
#P connect 22 4 29 0;
#P pop;
#P newobj 13 198 38 196617 p;
#N vpatcher 139 281 918 695;
#P window setfont "Sans Serif" 9.;
#P message 367 268 142 196617 setpixel 254 127 255 255 0;
#P newex 340 211 20 196617 t b;
#P message 362 229 186 196617 linesegment 250 127 254 129 0 255 0;
#P message 380 192 174 196617 linesegment 253 \$2 254 \$1 0 0 255;
#P newex 473 147 48 196617 pack 1 2;
#P newex 511 112 27 196617 int;
#P newex 463 82 58 196617 t i i b;
#P newex 463 55 104 196617 scale -0.1 0.1 128 0;
#P inlet 463 35 15 0;
#P message 178 190 174 196617 linesegment 253 \$2 254 \$1 0 255 0;
#P newex 271 145 48 196617 pack 1 2;
#P newex 309 110 27 196617 int;
#P newex 261 80 58 196617 t i i b;
#P newex 261 53 104 196617 scale -0.1 0.1 128 0;
#P inlet 261 33 15 0;
#P newex 91 146 48 196617 pack 1 2;
#P newex 129 111 27 196617 int;
#P newex 81 81 58 196617 t i i b;
#P newex 81 54 104 196617 scale -0.1 0.1 128 0;
#P message 91 170 309 196617 scrollrect 1 0 255 255 -1 0 \, linesegment 253 \$2 254 \$1 255 0 0;
#P inlet 81 34 15 0;
#P outlet 91 202 15 0;
#P connect 1 0 3 0;
#P connect 3 0 4 0;
#P fasten 4 0 6 0 86 134 96 134;
#P connect 6 0 2 0;
#P connect 18 0 0 0;
#P connect 21 0 0 0;
#P connect 2 0 0 0;
#P connect 12 0 0 0;
#P connect 4 2 5 0;
#P fasten 5 0 6 1 134 134 134 134;
#P fasten 4 1 5 1 110 104 151 104;
#P connect 11 0 12 0;
#P connect 7 0 8 0;
#P connect 8 0 9 0;
#P fasten 9 0 11 0 266 133 276 133;
#P connect 9 2 10 0;
#P fasten 10 0 11 1 314 133 314 133;
#P fasten 9 1 10 1 290 103 331 103;
#P connect 18 0 20 0;
#P connect 20 0 19 0;
#P connect 1 0 21 0;
#P connect 17 0 18 0;
#P connect 13 0 14 0;
#P connect 14 0 15 0;
#P fasten 15 0 17 0 468 135 478 135;
#P connect 15 2 16 0;
#P fasten 16 0 17 1 516 135 516 135;
#P fasten 15 1 16 1 492 105 533 105;
#P pop;
#P newobj 436 28 55 196617 p draw;
#P user lcd 543 41 273 122 1 0 1 0 0;
#P comment 397 66 100 196617 gravity constant;
#P comment 238 41 100 196617 intial conditions;
#P comment 580 209 100 196617 total energy;
#P comment 364 231 100 196617 potential energy;
#P newex 206 278 22 196617 r K;
#P flonum 286 231 69 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 450 182 22 196617 r K;
#P message 365 66 30 196617 -0.1;
#P newex 365 87 22 196617 s K;
#P hidden newex 0 231 26 196617 r go;
#P newex 160 21 26 196617 r go;
#P newex 328 86 26 196617 s go;
#P newex 277 86 30 196617 s x0;
#P message 232 65 37 196617 0. 0.1;
#P message 277 64 48 196617 10. -0.1;
#P newex 160 128 30 196617 r x0;
#P newex 92 42 30 196617 r v0;
#P newex 232 88 30 196617 s v0;
#P newex 59 394 49 196617 delay 10;
#P newex 81 418 36 196617 zl reg;
#P newex 92 369 40 196617 t b l l;
#P button 328 27 27 0;
#P message 160 43 31 196617 0. 0.;
#P newex 92 300 125 196617 vexpr $f1*$f1*$f2*$f3;
#P newex 92 255 27 196617 t f f;
#P newex 92 211 96 196617 t l l;
#P hidden message 0 258 70 196617 scalarmode 1;
#P newex 109 278 79 196617 vexpr $f1*$f2;
#P flonum 505 207 72 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 505 182 27 196617 + 1.;
#P flonum 288 153 68 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 288 128 141 196617 expr ($f1*$f1+$f2*$f2)/2.;
#P newex 286 207 175 196617 expr $f3/(sqrt($f1*$f1+$f2*$f2));
#N vpatcher 395 73 1173 587;
#P origin -159 0;
#P window setfont "Sans Serif" 9.;
#P newex 449 182 43 196617 r space;
#P toggle 422 185 15 0;
#P newex 416 215 29 196617 gate;
#P newex 426 137 26 196617 r go;
#P newex 570 407 48 196617 pack 1 2;
#P newex 518 408 48 196617 pack 1 2;
#P newex 466 407 48 196617 pack 1 2;
#P newex 414 408 48 196617 pack 1 2;
#P newex 354 406 48 196617 pack 1 2;
#P newex 300 408 48 196617 pack 1 2;
#P newex 246 407 48 196617 pack 1 2;
#P newex 192 411 48 196617 pack 1 2;
#P newex 142 413 48 196617 pack 1 2;
#P newex 90 414 48 196617 pack 1 2;
#P newex 33 410 48 196617 pack 1 2;
#P message 183 466 115 196617 setpixel \$1 \$2 255 0 0;
#P newex 313 33 64 196617 unpack 1. 2.;
#P message 366 134 34 196617 reset;
#P newex 266 189 27 196617 t l b;
#P newex 73 335 376 196617 unpack 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26;
#P newex 184 298 27 196617 t l l;
#P newex 81 286 366 196617 pack 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26;
#P number 169 113 65 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P number 496 129 65 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P newex 421 108 27 196617 - 1;
#P newex 373 108 27 196617 + 1;
#P newex 289 104 27 196617 - 1;
#P newex 241 104 27 196617 + 1;
#P newex 375 70 104 196617 scale -50. 50. 0 255;
#P newex 250 146 78 196617 pack 1. 2. 3. 4.;
#P newex 244 70 104 196617 scale -50. 50. 0 255;
#P message 250 170 140 196617 frameoval 126 126 128 128;
#P inlet 312 12 15 0;
#P outlet 299 228 15 0;
#P connect 14 2 19 0;
#P connect 14 3 19 1;
#P connect 13 1 14 0;
#P connect 11 0 12 0;
#P connect 14 4 20 0;
#P connect 10 0 12 1;
#P connect 14 0 12 2;
#P connect 14 1 12 3;
#P connect 14 5 20 1;
#P connect 14 2 12 4;
#P connect 14 6 21 0;
#P connect 14 3 12 5;
#P connect 14 4 12 6;
#P connect 3 0 11 0;
#P connect 14 5 12 7;
#P connect 14 7 21 1;
#P connect 27 0 18 0;
#P connect 28 0 18 0;
#P connect 29 0 18 0;
#P connect 26 0 18 0;
#P connect 25 0 18 0;
#P connect 24 0 18 0;
#P connect 23 0 18 0;
#P connect 22 0 18 0;
#P connect 21 0 18 0;
#P connect 20 0 18 0;
#P connect 19 0 18 0;
#P fasten 12 0 13 0 86 396 135 396 135 265 189 265;
#P connect 14 8 22 0;
#P connect 14 6 12 8;
#P connect 14 7 12 9;
#P connect 14 8 12 10;
#P connect 14 9 22 1;
#P connect 14 9 12 11;
#P connect 3 0 6 0;
#P connect 17 0 3 0;
#P connect 14 10 23 0;
#P connect 14 10 12 12;
#P connect 6 0 4 0;
#P connect 4 0 2 0;
#P connect 14 11 12 13;
#P connect 2 0 15 0;
#P connect 8 0 4 1;
#P connect 14 12 12 14;
#P connect 14 11 23 1;
#P connect 3 0 7 0;
#P connect 14 13 12 15;
#P connect 7 0 4 2;
#P connect 18 0 0 0;
#P connect 16 0 0 0;
#P connect 15 0 0 0;
#P connect 14 12 24 0;
#P connect 14 14 12 16;
#P connect 1 0 17 0;
#P connect 9 0 4 3;
#P connect 14 15 12 17;
#P connect 14 16 12 18;
#P connect 14 13 24 1;
#P connect 14 17 12 19;
#P connect 14 14 25 0;
#P connect 14 18 12 20;
#P connect 30 0 16 0;
#P connect 31 0 16 0;
#P connect 5 0 8 0;
#P connect 17 1 5 0;
#P connect 14 19 12 21;
#P connect 14 20 12 22;
#P connect 14 15 25 1;
#P connect 14 21 12 23;
#P connect 14 16 26 0;
#P connect 32 0 31 0;
#P connect 14 22 12 24;
#P connect 5 0 9 0;
#P connect 33 0 32 0;
#P connect 14 23 12 25;
#P connect 15 1 31 1;
#P connect 14 17 26 1;
#P connect 14 18 27 0;
#P fasten 5 0 10 0 501 84;
#P connect 14 19 27 1;
#P connect 14 20 28 0;
#P connect 14 21 28 1;
#P connect 14 22 29 0;
#P connect 14 23 29 1;
#P pop;
#P newobj 263 258 55 196617 p draw;
#P newex 92 233 160 196617 expr 1./sqrt($f1*$f1+$f2*$f2);
#P newex 92 175 36 196617 zl reg;
#P newex 92 152 78 196617 vexpr $f1+$f2;
#P newex 92 100 36 196617 zl reg;
#P newex 92 77 78 196617 vexpr $f1+$f2;
#P comment 360 154 100 196617 kinetic energy;
#P user panel 357 148 79 25;
#X brgb 200 128 128;
#X frgb 255 0 0;
#X border 1;
#X rounded 0;
#X shadow 0;
#X done;
#P user panel 358 225 89 25;
#X brgb 128 200 128;
#X frgb 0 255 0;
#X border 1;
#X rounded 0;
#X shadow 0;
#X done;
#P user panel 580 203 62 25;
#X brgb 128 128 200;
#X frgb 0 0 255;
#X border 1;
#X rounded 0;
#X shadow 0;
#X done;
#P user lcd 263 283 250 250 1 0 1 0 0;
#P window setfont "Sans Serif" 20.;
#P window linecount 3;
#P comment 620 286 120 196628 ARROW KEYS STEER SHIP;
#P hidden connect 35 0 18 0;
#P connect 35 0 49 0;
#P connect 49 0 48 0;
#P connect 18 0 47 0;
#P connect 9 0 47 1;
#P connect 48 0 47 2;
#P fasten 24 0 26 0 97 391 64 391;
#P fasten 26 0 25 0 64 414 86 414;
#P fasten 25 0 6 0 86 450 50 450 50 73 97 73;
#P connect 28 0 6 0;
#P connect 47 0 6 0;
#P connect 6 0 7 0;
#P connect 7 0 8 0;
#P connect 8 0 9 0;
#P connect 9 0 19 0;
#P connect 19 0 10 0;
#P connect 10 0 20 0;
#P hidden connect 18 0 21 0;
#P connect 20 0 21 0;
#P connect 21 0 24 0;
#P connect 24 1 25 1;
#P connect 20 1 17 0;
#P hidden connect 18 0 17 0;
#P fasten 17 0 21 1 114 297 154 297;
#P connect 34 0 22 0;
#P fasten 7 0 6 1 97 124 184 124 184 70 165 70;
#P connect 22 0 6 1;
#P fasten 9 0 8 1 97 199 184 199 184 149 165 149;
#P connect 29 0 8 1;
#P fasten 19 1 17 1 183 258 183 258;
#P connect 40 0 21 2;
#P fasten 23 0 31 0 333 60 237 60;
#P connect 31 0 27 0;
#P fasten 9 0 11 0 97 199 268 199;
#P connect 11 0 1 0;
#P fasten 23 0 30 0 333 60 282 60;
#P connect 30 0 32 0;
#P fasten 9 0 12 0 97 199 291 199;
#P connect 12 0 39 0;
#P fasten 7 0 13 0 97 124 293 124;
#P connect 13 0 14 0;
#P connect 23 0 33 0;
#P fasten 23 0 37 0 333 60 370 60;
#P connect 37 0 36 0;
#P connect 14 0 46 0;
#P connect 38 0 12 2;
#P connect 39 0 46 1;
#P connect 16 0 46 2;
#P fasten 14 0 15 0 293 175 510 175;
#P connect 15 0 16 0;
#P fasten 39 0 15 1 291 251 643 251 643 174 527 174;
#P fasten 46 0 45 0 441 50 531 50 531 29 548 29;
#P pop;
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