-
Notifications
You must be signed in to change notification settings - Fork 4
/
Copy pathnbody.nim
113 lines (100 loc) · 3.34 KB
/
nbody.nim
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
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
# From https://gist.github.com/idlewan/ab53b761ab1522251682
import os, strutils, math
const SOLAR_MASS = 4'f64 * PI * PI
const DAYS_PER_YEAR = 365.24'f64
type Planet = tuple[
x, y, z: float64,
dump: float64,
vx, vy, vz: float64,
mass: float64
]
var bodies: array[0..4, Planet] = [
# sun
(0'f64, 0'f64, 0'f64,
0'f64,
0'f64, 0'f64, 0'f64, SOLAR_MASS),
# jupiter
(4.84143144246472090e+00'f64,
-1.16032004402742839e+00'f64,
-1.03622044471123109e-01'f64,
0'f64,
1.66007664274403694e-03'f64 * DAYS_PER_YEAR,
7.69901118419740425e-03'f64 * DAYS_PER_YEAR,
-6.90460016972063023e-05'f64 * DAYS_PER_YEAR,
9.54791938424326609e-04'f64 * SOLAR_MASS),
# saturn
(8.34336671824457987e+00'f64,
4.12479856412430479e+00'f64,
-4.03523417114321381e-01'f64,
0'f64,
-2.76742510726862411e-03'f64 * DAYS_PER_YEAR,
4.99852801234917238e-03'f64 * DAYS_PER_YEAR,
2.30417297573763929e-05'f64 * DAYS_PER_YEAR,
2.85885980666130812e-04'f64 * SOLAR_MASS),
# uranus
(1.28943695621391310e+01'f64,
-1.51111514016986312e+01'f64,
-2.23307578892655734e-01'f64,
0'f64,
2.96460137564761618e-03'f64 * DAYS_PER_YEAR,
2.37847173959480950e-03'f64 * DAYS_PER_YEAR,
-2.96589568540237556e-05'f64 * DAYS_PER_YEAR,
4.36624404335156298e-05'f64 * SOLAR_MASS),
# neptune
(1.53796971148509165e+01'f64,
-2.59193146099879641e+01'f64,
1.79258772950371181e-01'f64,
0'f64,
2.68067772490389322e-03'f64 * DAYS_PER_YEAR,
1.62824170038242295e-03'f64 * DAYS_PER_YEAR,
-9.51592254519715870e-05'f64 * DAYS_PER_YEAR,
5.15138902046611451e-05'f64 * SOLAR_MASS)
]
proc advance(bodies: var array[0..4, Planet], dt: float64) =
for i in 0 .. <bodies.len:
var b = addr bodies[i]
for j in i+1 .. <bodies.len:
var b2 = addr bodies[j]
let dx = b.x - b2.x
let dy = b.y - b2.y
let dz = b.z - b2.z
let distance = sqrt(dx*dx + dy*dy + dz*dz)
let mag = dt / (distance*distance*distance)
b.vx -= dx * b2.mass * mag
b.vy -= dy * b2.mass * mag
b.vz -= dz * b2.mass * mag
b2.vx += dx * b.mass * mag
b2.vy += dy * b.mass * mag
b2.vz += dz * b.mass * mag
for i in 0 .. <bodies.len:
var b = addr bodies[i]
b.x += dt * b.vx
b.y += dt * b.vy
b.z += dt * b.vz
proc energy(bodies: var array[0..4, Planet]): float64 =
for i, b in bodies:
result += 0.5 * b.mass * (b.vx*b.vx + b.vy*b.vy + b.vz*b.vz)
for j in i+1 .. <bodies.len:
let b2 = bodies[j]
let dx = b.x - b2.x
let dy = b.y - b2.y
let dz = b.z - b2.z
let distance = sqrt(dx*dx + dy*dy + dz*dz)
result -= b.mass * b2.mass / distance
proc offset_momentum(bodies: var array[0..4, Planet]) =
var px, py, pz: float64
for b in bodies:
px += b.vx * b.mass
py += b.vy * b.mass
pz += b.vz * b.mass
bodies[0].vx = -px / SOLAR_MASS
bodies[0].vy = -py / SOLAR_MASS
bodies[0].vz = -pz / SOLAR_MASS
var n = 1_000_000
if paramCount() > 0:
n = paramStr(1).parseInt
offset_momentum(bodies)
echo formatFloat(energy(bodies), precision=9)
for i in 1 .. n:
advance(bodies, 0.01)
echo formatFloat(energy(bodies), precision=9)