|\^/|     Maple 2020 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2020
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> with(LinearAlgebra):
> Digits := 12;
                                  Digits := 12


> init := proc()
> global particle1, particle2, particle3, world;
>     particle1 := table():
>     particle2 := table():
>     particle3 := table():
>     
>     particle1[name] := "particle1":
>     particle1[mass] := 1.3:
>     particle1[charge] := 3.3:
>     particle1[location] := <1.0,2.0,3.0>:
>     particle1[velocity] := <1.0,2.0,3.0>:
>     particle1[name] := "particle1":
>     
>     particle2[name] := "particle2":
>     particle2[mass] := 2.3:
>     particle2[charge] := 4.3:
>     particle2[location] := <8.0,1.0,2.0>:
>     particle2[velocity] := <7.0,-3.0,0.0>:
>     
>     particle3[name] := "particle3":
>     particle3[mass] := 4.1:
>     particle3[charge] := -2.3:
>     particle3[location] := <-8.0,-1.0,2.0>:
>     particle3[velocity] := <5.0,3.0,0.0>:
>     
>     world := {particle1, particle2, particle3}:

> end;
init := proc()
global particle1, particle2, particle3, world;
    particle1 := table();
    particle2 := table();
    particle3 := table();
    particle1[name] := "particle1";
    particle1[mass] := 1.3;
    particle1[charge] := 3.3;
    particle1[location] := <1.0, 2.0, 3.0>;
    particle1[velocity] := <1.0, 2.0, 3.0>;
    particle1[name] := "particle1";
    particle2[name] := "particle2";
    particle2[mass] := 2.3;
    particle2[charge] := 4.3;
    particle2[location] := <8.0, 1.0, 2.0>;
    particle2[velocity] := <7.0, -3.0, 0.>;
    particle3[name] := "particle3";
    particle3[mass] := 4.1;
    particle3[charge] := -2.3;
    particle3[location] := <-8.0, -1.0, 2.0>;
    particle3[velocity] := <5.0, 3.0, 0.>;
    world := {particle1, particle2, particle3}
end proc


> external_world := proc(w, p) w minus {p};
> end;
               external_world := proc(w, p) w minus {p} end proc


> ewp1 := external_world(world, particle1);
                        ewp1 := world minus {particle1}

> ewp2 := external_world(world, particle2);
                        ewp2 := world minus {particle2}

> ewp3 := external_world(world, particle3);
                        ewp3 := world minus {particle3}


# field (Vector) of gravity caused by p2 at p1
> gravity := proc(p2, p1)
> local G;
>     G := 6.67E-3; # changed to have greater effect
>     G * p2[mass] * (p2[location] - p1[location]) / DotProduct(p2[location], p1[location]);
> end:

# Add to Set of gravity Vectors at p1
> union_to_physical_feeling_grav := proc(p)
>     local p2;
>     p[physical_feeling_grav] := {};
>     for p2 in external_world(world, p) do
>         p[physical_feeling_grav] := p[physical_feeling_grav] union {gravity(p2, p)};
>     od;
>     return 0;
> end:

# Add to Sum of gravity Vectors at p1
> sum_to_body_grav := proc(p)
>     local p2;
>     p[body_grav] := <0.0, 0.0, 0.0>;
>     for p2 in external_world(world, p) do
>         p[body_grav] := p[body_grav] + gravity(p2, p);
>     od;
>     return 0;
> end:


# out := map(union_to_physical_feeling_grav, world):
# out2 := map(sum_to_body_grav, world):


> jump := proc(delta_time)
> global particle1, particle2, particle3, world;
> local out, out2, particle;
>     for particle in world do
>         particle[acceleration] := particle[body_grav]
>         / particle[mass];
>         particle[location] := particle[location]
>         + particle[velocity] * delta_time;
>         particle[velocity] := particle[velocity]
>         + particle[acceleration] * delta_time;
>         out := map(union_to_physical_feeling_grav, world):
>         out2 := map(sum_to_body_grav, world):
>     od;
> end;
jump := proc(delta_time)
local out, out2, particle;
global particle1, particle2, particle3, world;
    for particle in world do
        particle[acceleration] := particle[body_grav]/particle[mass];
        particle[location] :=
            particle[location] + particle[velocity]*delta_time;
        particle[velocity] :=
            particle[velocity] + particle[acceleration]*delta_time;
        out := map(union_to_physical_feeling_grav, world);
        out2 := map(sum_to_body_grav, world)
    end do
end proc


> run := proc(start_time, end_time, delta_time)
> global particle1, particle2, particle3, world;
> local world_time, out, out2;
>     world_time := start_time;
>     init();
>     out := map(union_to_physical_feeling_grav, world):
>     out2 := map(sum_to_body_grav, world):
>     while world_time <= end_time do
>         print("world_time = ", world_time);
>         map(print, evalf(world));
>         jump(delta_time);
>         world_time := world_time + delta_time;
>     od;
> end;
run := proc(start_time, end_time, delta_time)
local world_time, out, out2;
global particle1, particle2, particle3, world;
    world_time := start_time;
    init();
    out := map(union_to_physical_feeling_grav, world);
    out2 := map(sum_to_body_grav, world);
    while world_time <= end_time do
        print("world_time = ", world_time);
        map(print, evalf(world));
        jump(delta_time);
        world_time := world_time + delta_time
    end do
end proc


> run(0.0, 0.4, 0.1);
                              "world_time = ", 0.

memory used=3.3MB, alloc=40.3MB, time=0.05
                               [0.0682424375000000 ]
                               [                   ]
table([mass = 1.3, body_grav = [0.0195514375000000 ], charge = 3.3,
                               [                   ]
                               [0.00587793750000000]

                                   [1.0]             [1.0]
                                   [   ]             [   ]
    name = "particle1", location = [2.0], velocity = [2.0],
                                   [   ]             [   ]
                                   [3.0]             [3.0]

                             [ 0.00671168750000000 ]  [0.0615307500000000 ]
                             [                     ]  [                   ]
    physical_feeling_grav = {[-0.000958812500000000], [0.0205102500000000 ]}
                             [                     ]  [                   ]
                             [-0.000958812500000000]  [0.00683675000000000]

    ])

                               [0.00337942110657890 ]
                               [                    ]
table([mass = 2.3, body_grav = [0.00143856045082236 ], charge = 4.3,
                               [                    ]
                               [0.000541937500000000]

                                   [8.0]             [7.0 ]
                                   [   ]             [    ]
    name = "particle2", location = [1.0], velocity = [-3.0],
                                   [   ]             [    ]
                                   [2.0]             [ 0. ]

                             [-0.00379356250000000]  [0.00717298360657890 ]
                             [                    ]  [                    ]
    physical_feeling_grav = {[0.000541937500000000], [0.000896622950822362]}
                             [                    ]  [                    ]
                             [0.000541937500000000]  [        -0.         ]

    ])

                               [-0.0235336188524711 ]
                               [                    ]
table([mass = 4.1, body_grav = [-0.00700623360655889], charge = -2.3,
                               [                    ]
                               [-0.00216775000000000]

                                   [-8.0]             [5.0]
                                   [    ]             [   ]
    name = "particle3", location = [-1.0], velocity = [3.0],
                                   [    ]             [   ]
                                   [2.0 ]             [0. ]

                             [-0.0195097500000000 ]  [-0.00402386885247109 ]
                             [                    ]  [                     ]
    physical_feeling_grav = {[-0.00650325000000000], [-0.000502983606558886]}
                             [                    ]  [                     ]
                             [-0.00216775000000000]  [         -0.         ]

    ])

                              "world_time = ", 0.1

                               [0.0803088311687275]
                               [                  ]
table([mass = 1.3, body_grav = [0.0235615584415221],
                               [                  ]
                               [0.0100184415584251]

                   [0.0524941826923234 ]
                   [                   ]
    acceleration = [0.0150395673076968 ], charge = 3.3, name = "particle1",
                   [                   ]
                   [0.00452149038461674]

               [1.10000000000000]             [1.00524941826923]
               [                ]             [                ]
    location = [2.20000000000000], velocity = [2.00150395673077],
               [                ]             [                ]
               [3.30000000000000]             [3.00045214903846]

                             [0.00658337662337916 ]  [0.0737254545453484]
                             [                    ]  [                  ]
    physical_feeling_grav = {[-0.00129935064935115], [0.0248609090908733]}
                             [                    ]  [                  ]
                             [-0.00112610389610433]  [0.0111445454545294]

    ])

                               [0.00345455870661351 ]
                               [                    ]
table([mass = 2.3, body_grav = [0.00135452896310201 ],
                               [                    ]
                               [0.000636493506493752]

                   [0.00164067716096400 ]
                   [                    ]
    acceleration = [0.000646881520120994], charge = 4.3, name = "particle2",
                   [                    ]
                   [0.000278465909091221]

               [8.70000000000000 ]             [  7.00016406771610   ]
               [                 ]             [                     ]
    location = [0.700000000000000], velocity = [  -2.99993531184799  ],
               [                 ]             [                     ]
               [       2.        ]             [0.0000278465909091221]

                             [-0.00372103896104040]  [0.00717559766765391 ]
                             [                    ]  [                    ]
    physical_feeling_grav = {[0.000734415584415868], [0.000620113378686140]}
                             [                    ]  [                    ]
                             [0.000636493506493752]  [        -0.         ]

    ])

                               [-0.0274016989133066 ]
                               [                    ]
table([mass = 4.1, body_grav = [-0.00823059575344229],
                               [                    ]
                               [-0.00353363636363127]

                   [-0.00531643365839788 ]
                   [                     ]
    acceleration = [-0.00163403433964316 ], charge = -2.3, name = "particle3",
                   [                     ]
                   [-0.000624850332593985]

               [-7.50000000000000 ]             [   4.99946835663416   ]
               [                  ]             [                      ]
    location = [-0.700000000000000], velocity = [   2.99983659656604   ],
               [                  ]             [                      ]
               [        2.        ]             [-0.0000624850332593985]

                             [-0.0233763636363300 ]  [-0.00402533527697658 ]
                             [                    ]  [                     ]
    physical_feeling_grav = {[-0.00788272727271592], [-0.000347868480726371]}
                             [                    ]  [                     ]
                             [-0.00353363636363127]  [         -0.         ]

    ])

                              "world_time = ", 0.2

                               [0.110112633455194 ]
                               [                  ]
table([mass = 1.3, body_grav = [0.0338121698275561],
                               [                  ]
                               [0.0189600602410868]

                   [0.0617760239759628 ]
                   [                   ]
    acceleration = [0.0181242757242532 ], charge = 3.3, name = "particle1",
                   [                   ]
                   [0.00770649350648314]

               [1.20052494182692]             [1.01142702066683]
               [                ]             [                ]
    location = [2.40015039567308], velocity = [2.00331638430319],
               [                ]             [                ]
               [3.60004521490385]             [3.00122279838911]

                             [0.00646888946971501 ]  [0.103643743985479 ]
                             [                    ]  [                  ]
    physical_feeling_grav = {[-0.00157798932307964], [0.0353901591506357]}
                             [                    ]  [                  ]
                             [-0.00126233409381045]  [0.0202223943348973]

    ])

                               [0.00358202071310777 ]
                               [                    ]
table([mass = 2.3, body_grav = [0.00124500579956557 ],
                               [                    ]
                               [0.000713497170342820]

                   [0.00165677885560210 ]
                   [                    ]
    acceleration = [0.000601290874607766], charge = 4.3, name = "particle2",
                   [                    ]
                   [0.000312147194437600]

               [9.40001640677161 ]             [  7.00032974560166   ]
               [                 ]             [                     ]
    location = [0.400006468815201], velocity = [  -2.99987518276053  ],
               [                 ]             [                     ]
               [2.00000278465909 ]             [0.0000590613103528821]

                             [-0.00365632883070848]  [ 0.00723834954381625  ]
                             [                    ]  [                      ]
    physical_feeling_grav = {[0.000891907008697187], [ 0.000353098790868387 ]}
                             [                    ]  [                      ]
                             [0.000713493183458083]  [                    -8]
                                                     [0.398688473697724 10  ]

    ])

                               [-0.0369231880809512 ]
                               [                    ]
table([mass = 4.1, body_grav = [-0.0114193497841033 ],
                               [                    ]
                               [-0.00641198092809790]

                   [-0.00622842865864197 ]
                   [                     ]
    acceleration = [-0.00194353103718458 ], charge = -2.3, name = "particle3",
                   [                     ]
                   [-0.000971282363307742]

               [-7.00005316433658 ]             [  4.99884551376830   ]
               [                  ]             [                     ]
    location = [-0.400016340343396], velocity = [  2.99964224346232   ],
               [                  ]             [                     ]
               [ 1.99999375149667 ]             [-0.000159613269590173]

                             [-0.0328626505319811 ]  [ -0.00406053754897009  ]
                             [                    ]  [                       ]
    physical_feeling_grav = {[-0.0112212699745918 ], [ -0.000198079809511534 ]}
                             [                    ]  [                       ]
                             [-0.00641197869155280]  [                     -8]
                                                     [-0.223654509635309 10  ]

    ])

                              "world_time = ", 0.3

                               [0.238023735154420 ]
                               [                  ]
table([mass = 1.3, body_grav = [0.0783779091144403],
                               [                  ]
                               [0.0550476084948090]

                   [0.0847020257347899]
                   [                  ]
    acceleration = [0.0260093614058202], charge = 3.3, name = "particle1",
                   [                  ]
                   [0.0145846617239173]

               [1.30166764389361]             [1.01989722324031]
               [                ]             [                ]
    location = [2.60048203410340], velocity = [2.00591732044378],
               [                ]             [                ]
               [3.90016749474276]             [3.00268126456150]

                             [0.00636457749017699 ]  [0.231659157664243 ]
                             [                    ]  [                  ]
    physical_feeling_grav = {[-0.00180878615313472], [0.0801866952675750]}
                             [                    ]  [                  ]
                             [-0.00137453776300003]  [0.0564221462578090]

    ])

                               [0.00376479374130605 ]
                               [                    ]
table([mass = 2.3, body_grav = [0.00111108851054096 ],
                               [                    ]
                               [0.000776926353015814]

                   [0.00169852201097442 ]
                   [                    ]
    acceleration = [0.000547129745324395], charge = 4.3, name = "particle2",
                   [                    ]
                   [0.000339892370574309]

               [10.1000493813318 ]             [  7.00049959780275   ]
               [                 ]             [                     ]
    location = [0.100018950539148], velocity = [  -2.99982046978600  ],
               [                 ]             [                     ]
               [2.00000869079013 ]             [0.0000930505474103130]

                             [-0.00359736988575221]  [ 0.00736216362705826  ]
                             [                    ]  [                      ]
    physical_feeling_grav = {[0.00102235739090223 ], [0.0000887311196387250 ]}
                             [                    ]  [                      ]
                             [0.000776912648652189]  [                    -7]
                                                     [0.137043636247700 10  ]

    ])

                               [-0.0775828978794512]
                               [                   ]
table([mass = 4.1, body_grav = [-0.0254748257129309],
                               [                   ]
                               [-0.0178899565012654]

                   [-0.00842450706171980]
                   [                    ]
    acceleration = [-0.00272641182274136], charge = -2.3, name = "particle3",
                   [                    ]
                   [-0.00170884612073074]

               [-6.50016861295975 ]             [  4.99800306306212   ]
               [                  ]             [                     ]
    location = [-0.100052115997165], velocity = [  2.99936960228004   ],
               [                  ]             [                     ]
               [ 1.99997779016972 ]             [-0.000330497881663247]

                             [-0.0734529036496380]  [ -0.00412999422981317  ]
                             [                   ]  [                       ]
    physical_feeling_grav = {[-0.0254250497189872], [-0.0000497759939436750 ]}
                             [                   ]  [                       ]
                             [-0.0178899488134516]  [                     -8]
                                                    [-0.768781374072463 10  ]

    ])

                              "world_time = ", 0.4

                               [-0.370036593234108]
                               [                  ]
table([mass = 1.3, body_grav = [-0.134205069779875],
                               [                  ]
                               [-0.113305899064845]

                   [0.183095180888070 ]
                   [                  ]
    acceleration = [0.0602906993188183], charge = 3.3, name = "particle1",
                   [                  ]
                   [0.0423443142267889]

               [1.40365736621764]             [1.03820674132911]
               [                ]             [                ]
    location = [2.80107376614777], velocity = [2.01194639037566],
               [                ]             [                ]
               [4.20043562119891]             [3.00691569598418]

                             [0.00626729751510984 ]  [-0.376303890749218]
                             [                    ]  [                  ]
    physical_feeling_grav = {[-0.00200165029719745], [-0.132203419482678]}
                             [                    ]  [                  ]
                             [-0.00146764828138475]  [-0.111838250783460]

    ])

                               [0.00400869134679056 ]
                               [                    ]
table([mass = 2.3, body_grav = [0.000951653362565911],
                               [                    ]
                               [0.000829573258089894]

                   [0.00176663816250709 ]
                   [                    ]
    acceleration = [0.000484065771395824], charge = 4.3, name = "particle2",
                   [                    ]
                   [0.000362924044527925]

               [ 10.8000993411121 ]             [  7.00067626161901  ]
               [                  ]             [                    ]
    location = [-0.199963096439451], velocity = [ -2.99977206320886  ],
               [                  ]             [                    ]
               [ 2.00001799584487 ]             [0.000129342951863105]

                             [-0.00354238555201861]  [ 0.00755107689880917  ]
                             [                    ]  [                      ]
    physical_feeling_grav = {[0.00113136755928551 ], [-0.000179714196719602 ]}
                             [                    ]  [                      ]
                             [0.000829540332956596]  [                    -7]
                                                     [0.329251332982611 10  ]

    ])

                               [0.115079897830908 ]
                               [                  ]
table([mass = 4.1, body_grav = [0.0420189726780333],
                               [                  ]
                               [0.0354608903148029]

                   [-0.0176356689989635 ]
                   [                    ]
    acceleration = [-0.00610857103664651], charge = -2.3, name = "particle3",
                   [                    ]
                   [-0.00463754059620181]

               [-6.00036830665354]             [  4.99623949616223   ]
               [                 ]             [                     ]
    location = [0.199884844230840], velocity = [  2.99875874517638   ],
               [                 ]             [                     ]
               [1.99994474038155 ]             [-0.000794251941283428]

                             [0.119315867798532 ]  [ -0.00423596996762466  ]
                             [                  ]  [                       ]
    physical_feeling_grav = {[0.0419181573969467], [ 0.000100815281086606  ]}
                             [                  ]  [                       ]
                             [0.0354609087849996]  [                     -7]
                                                   [-0.184701967282928 10  ]

    ])

                                      0.5



> quit;
memory used=6.2MB, alloc=40.3MB, time=0.07