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@KeithHanson
Last active April 18, 2024 15:02
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2D physics simulation of 10 bodies, 5 at rest and 5 in motion, using clingo and ASP
┌─[user@linux-gpu] - [~] - [2024-04-18 09:54:56]
└─[0] <> clingo test.pl --out-ifs=\\n
clingo version 5.4.1
Reading from test.pl
Solving...
Answer: 1
position_x(1,0,0)
position_x(2,0,0)
position_x(3,0,0)
position_x(4,0,0)
position_x(5,0,0)
position_x(6,0,0)
position_x(7,0,0)
position_x(8,0,0)
position_x(9,0,0)
position_x(10,0,0)
position_x(10,0,1)
position_x(9,0,1)
position_x(8,0,1)
position_x(7,0,1)
position_x(6,0,1)
position_x(5,10,1)
position_x(4,10,1)
position_x(3,10,1)
position_x(2,10,1)
position_x(1,10,1)
position_x(1,30,2)
position_x(2,30,2)
position_x(3,30,2)
position_x(4,30,2)
position_x(5,30,2)
position_x(6,0,2)
position_x(7,0,2)
position_x(8,0,2)
position_x(9,0,2)
position_x(10,0,2)
position_x(10,0,3)
position_x(9,0,3)
position_x(8,0,3)
position_x(7,0,3)
position_x(6,0,3)
position_x(5,60,3)
position_x(4,60,3)
position_x(3,60,3)
position_x(2,60,3)
position_x(1,60,3)
position_x(1,100,4)
position_x(2,100,4)
position_x(3,100,4)
position_x(4,100,4)
position_x(5,100,4)
position_x(6,0,4)
position_x(7,0,4)
position_x(8,0,4)
position_x(9,0,4)
position_x(10,0,4)
position_x(10,0,5)
position_x(9,0,5)
position_x(8,0,5)
position_x(7,0,5)
position_x(6,0,5)
position_x(5,150,5)
position_x(4,150,5)
position_x(3,150,5)
position_x(2,150,5)
position_x(1,150,5)
position_x(1,210,6)
position_x(2,210,6)
position_x(3,210,6)
position_x(4,210,6)
position_x(5,210,6)
position_x(6,0,6)
position_x(7,0,6)
position_x(8,0,6)
position_x(9,0,6)
position_x(10,0,6)
position_x(10,0,7)
position_x(9,0,7)
position_x(8,0,7)
position_x(7,0,7)
position_x(6,0,7)
position_x(5,280,7)
position_x(4,280,7)
position_x(3,280,7)
position_x(2,280,7)
position_x(1,280,7)
position_x(1,360,8)
position_x(2,360,8)
position_x(3,360,8)
position_x(4,360,8)
position_x(5,360,8)
position_x(6,0,8)
position_x(7,0,8)
position_x(8,0,8)
position_x(9,0,8)
position_x(10,0,8)
position_x(10,0,9)
position_x(9,0,9)
position_x(8,0,9)
position_x(7,0,9)
position_x(6,0,9)
position_x(5,450,9)
position_x(4,450,9)
position_x(3,450,9)
position_x(2,450,9)
position_x(1,450,9)
position_x(1,550,10)
position_x(2,550,10)
position_x(3,550,10)
position_x(4,550,10)
position_x(5,550,10)
position_x(6,0,10)
position_x(7,0,10)
position_x(8,0,10)
position_x(9,0,10)
position_x(10,0,10)
position_x(10,0,11)
position_x(9,0,11)
position_x(8,0,11)
position_x(7,0,11)
position_x(6,0,11)
position_x(5,660,11)
position_x(4,660,11)
position_x(3,660,11)
position_x(2,660,11)
position_x(1,660,11)
position_x(1,780,12)
position_x(2,780,12)
position_x(3,780,12)
position_x(4,780,12)
position_x(5,780,12)
position_x(6,0,12)
position_x(7,0,12)
position_x(8,0,12)
position_x(9,0,12)
position_x(10,0,12)
position_x(10,0,13)
position_x(9,0,13)
position_x(8,0,13)
position_x(7,0,13)
position_x(6,0,13)
position_x(5,910,13)
position_x(4,910,13)
position_x(3,910,13)
position_x(2,910,13)
position_x(1,910,13)
position_x(1,1050,14)
position_x(2,1050,14)
position_x(3,1050,14)
position_x(4,1050,14)
position_x(5,1050,14)
position_x(6,0,14)
position_x(7,0,14)
position_x(8,0,14)
position_x(9,0,14)
position_x(10,0,14)
position_x(10,0,15)
position_x(9,0,15)
position_x(8,0,15)
position_x(7,0,15)
position_x(6,0,15)
position_x(5,1200,15)
position_x(4,1200,15)
position_x(3,1200,15)
position_x(2,1200,15)
position_x(1,1200,15)
position_x(1,1360,16)
position_x(2,1360,16)
position_x(3,1360,16)
position_x(4,1360,16)
position_x(5,1360,16)
position_x(6,0,16)
position_x(7,0,16)
position_x(8,0,16)
position_x(9,0,16)
position_x(10,0,16)
position_x(10,0,17)
position_x(9,0,17)
position_x(8,0,17)
position_x(7,0,17)
position_x(6,0,17)
position_x(5,1530,17)
position_x(4,1530,17)
position_x(3,1530,17)
position_x(2,1530,17)
position_x(1,1530,17)
position_x(1,1710,18)
position_x(2,1710,18)
position_x(3,1710,18)
position_x(4,1710,18)
position_x(5,1710,18)
position_x(6,0,18)
position_x(7,0,18)
position_x(8,0,18)
position_x(9,0,18)
position_x(10,0,18)
position_x(10,0,19)
position_x(9,0,19)
position_x(8,0,19)
position_x(7,0,19)
position_x(6,0,19)
position_x(5,1900,19)
position_x(4,1900,19)
position_x(3,1900,19)
position_x(2,1900,19)
position_x(1,1900,19)
position_x(1,2100,20)
position_x(2,2100,20)
position_x(3,2100,20)
position_x(4,2100,20)
position_x(5,2100,20)
position_x(6,0,20)
position_x(7,0,20)
position_x(8,0,20)
position_x(9,0,20)
position_x(10,0,20)
position_x(10,0,21)
position_x(9,0,21)
position_x(8,0,21)
position_x(7,0,21)
position_x(6,0,21)
position_x(5,2310,21)
position_x(4,2310,21)
position_x(3,2310,21)
position_x(2,2310,21)
position_x(1,2310,21)
position_x(1,2530,22)
position_x(2,2530,22)
position_x(3,2530,22)
position_x(4,2530,22)
position_x(5,2530,22)
position_x(6,0,22)
position_x(7,0,22)
position_x(8,0,22)
position_x(9,0,22)
position_x(10,0,22)
position_x(10,0,23)
position_x(9,0,23)
position_x(8,0,23)
position_x(7,0,23)
position_x(6,0,23)
position_x(5,2760,23)
position_x(4,2760,23)
position_x(3,2760,23)
position_x(2,2760,23)
position_x(1,2760,23)
position_x(1,3000,24)
position_x(2,3000,24)
position_x(3,3000,24)
position_x(4,3000,24)
position_x(5,3000,24)
position_x(6,0,24)
position_x(7,0,24)
position_x(8,0,24)
position_x(9,0,24)
position_x(10,0,24)
position_x(10,0,25)
position_x(9,0,25)
position_x(8,0,25)
position_x(7,0,25)
position_x(6,0,25)
position_x(5,3250,25)
position_x(4,3250,25)
position_x(3,3250,25)
position_x(2,3250,25)
position_x(1,3250,25)
position_x(1,3510,26)
position_x(2,3510,26)
position_x(3,3510,26)
position_x(4,3510,26)
position_x(5,3510,26)
position_x(6,0,26)
position_x(7,0,26)
position_x(8,0,26)
position_x(9,0,26)
position_x(10,0,26)
position_x(10,0,27)
position_x(9,0,27)
position_x(8,0,27)
position_x(7,0,27)
position_x(6,0,27)
position_x(5,3780,27)
position_x(4,3780,27)
position_x(3,3780,27)
position_x(2,3780,27)
position_x(1,3780,27)
position_x(1,4060,28)
position_x(2,4060,28)
position_x(3,4060,28)
position_x(4,4060,28)
position_x(5,4060,28)
position_x(6,0,28)
position_x(7,0,28)
position_x(8,0,28)
position_x(9,0,28)
position_x(10,0,28)
position_x(10,0,29)
position_x(9,0,29)
position_x(8,0,29)
position_x(7,0,29)
position_x(6,0,29)
position_x(5,4350,29)
position_x(4,4350,29)
position_x(3,4350,29)
position_x(2,4350,29)
position_x(1,4350,29)
position_x(1,4650,30)
position_x(2,4650,30)
position_x(3,4650,30)
position_x(4,4650,30)
position_x(5,4650,30)
position_x(6,0,30)
position_x(7,0,30)
position_x(8,0,30)
position_x(9,0,30)
position_x(10,0,30)
position_x(10,0,31)
position_x(9,0,31)
position_x(8,0,31)
position_x(7,0,31)
position_x(6,0,31)
position_x(5,4960,31)
position_x(4,4960,31)
position_x(3,4960,31)
position_x(2,4960,31)
position_x(1,4960,31)
position_x(1,5280,32)
position_x(2,5280,32)
position_x(3,5280,32)
position_x(4,5280,32)
position_x(5,5280,32)
position_x(6,0,32)
position_x(7,0,32)
position_x(8,0,32)
position_x(9,0,32)
position_x(10,0,32)
position_x(10,0,33)
position_x(9,0,33)
position_x(8,0,33)
position_x(7,0,33)
position_x(6,0,33)
position_x(5,5610,33)
position_x(4,5610,33)
position_x(3,5610,33)
position_x(2,5610,33)
position_x(1,5610,33)
position_x(1,5950,34)
position_x(2,5950,34)
position_x(3,5950,34)
position_x(4,5950,34)
position_x(5,5950,34)
position_x(6,0,34)
position_x(7,0,34)
position_x(8,0,34)
position_x(9,0,34)
position_x(10,0,34)
position_x(10,0,35)
position_x(9,0,35)
position_x(8,0,35)
position_x(7,0,35)
position_x(6,0,35)
position_x(5,6300,35)
position_x(4,6300,35)
position_x(3,6300,35)
position_x(2,6300,35)
position_x(1,6300,35)
position_x(1,6660,36)
position_x(2,6660,36)
position_x(3,6660,36)
position_x(4,6660,36)
position_x(5,6660,36)
position_x(6,0,36)
position_x(7,0,36)
position_x(8,0,36)
position_x(9,0,36)
position_x(10,0,36)
position_x(10,0,37)
position_x(9,0,37)
position_x(8,0,37)
position_x(7,0,37)
position_x(6,0,37)
position_x(5,7030,37)
position_x(4,7030,37)
position_x(3,7030,37)
position_x(2,7030,37)
position_x(1,7030,37)
position_x(1,7410,38)
position_x(2,7410,38)
position_x(3,7410,38)
position_x(4,7410,38)
position_x(5,7410,38)
position_x(6,0,38)
position_x(7,0,38)
position_x(8,0,38)
position_x(9,0,38)
position_x(10,0,38)
position_x(10,0,39)
position_x(9,0,39)
position_x(8,0,39)
position_x(7,0,39)
position_x(6,0,39)
position_x(5,7800,39)
position_x(4,7800,39)
position_x(3,7800,39)
position_x(2,7800,39)
position_x(1,7800,39)
position_x(1,8200,40)
position_x(2,8200,40)
position_x(3,8200,40)
position_x(4,8200,40)
position_x(5,8200,40)
position_x(6,0,40)
position_x(7,0,40)
position_x(8,0,40)
position_x(9,0,40)
position_x(10,0,40)
position_x(10,0,41)
position_x(9,0,41)
position_x(8,0,41)
position_x(7,0,41)
position_x(6,0,41)
position_x(5,8610,41)
position_x(4,8610,41)
position_x(3,8610,41)
position_x(2,8610,41)
position_x(1,8610,41)
position_x(1,9030,42)
position_x(2,9030,42)
position_x(3,9030,42)
position_x(4,9030,42)
position_x(5,9030,42)
position_x(6,0,42)
position_x(7,0,42)
position_x(8,0,42)
position_x(9,0,42)
position_x(10,0,42)
position_x(10,0,43)
position_x(9,0,43)
position_x(8,0,43)
position_x(7,0,43)
position_x(6,0,43)
position_x(5,9460,43)
position_x(4,9460,43)
position_x(3,9460,43)
position_x(2,9460,43)
position_x(1,9460,43)
position_x(1,9900,44)
position_x(2,9900,44)
position_x(3,9900,44)
position_x(4,9900,44)
position_x(5,9900,44)
position_x(6,0,44)
position_x(7,0,44)
position_x(8,0,44)
position_x(9,0,44)
position_x(10,0,44)
position_x(10,0,45)
position_x(9,0,45)
position_x(8,0,45)
position_x(7,0,45)
position_x(6,0,45)
position_x(5,10350,45)
position_x(4,10350,45)
position_x(3,10350,45)
position_x(2,10350,45)
position_x(1,10350,45)
position_x(1,10810,46)
position_x(2,10810,46)
position_x(3,10810,46)
position_x(4,10810,46)
position_x(5,10810,46)
position_x(6,0,46)
position_x(7,0,46)
position_x(8,0,46)
position_x(9,0,46)
position_x(10,0,46)
position_x(10,0,47)
position_x(9,0,47)
position_x(8,0,47)
position_x(7,0,47)
position_x(6,0,47)
position_x(5,11280,47)
position_x(4,11280,47)
position_x(3,11280,47)
position_x(2,11280,47)
position_x(1,11280,47)
position_x(1,11760,48)
position_x(2,11760,48)
position_x(3,11760,48)
position_x(4,11760,48)
position_x(5,11760,48)
position_x(6,0,48)
position_x(7,0,48)
position_x(8,0,48)
position_x(9,0,48)
position_x(10,0,48)
position_x(10,0,49)
position_x(9,0,49)
position_x(8,0,49)
position_x(7,0,49)
position_x(6,0,49)
position_x(5,12250,49)
position_x(4,12250,49)
position_x(3,12250,49)
position_x(2,12250,49)
position_x(1,12250,49)
position_x(1,12750,50)
position_x(2,12750,50)
position_x(3,12750,50)
position_x(4,12750,50)
position_x(5,12750,50)
position_x(6,0,50)
position_x(7,0,50)
position_x(8,0,50)
position_x(9,0,50)
position_x(10,0,50)
position_x(10,0,51)
position_x(9,0,51)
position_x(8,0,51)
position_x(7,0,51)
position_x(6,0,51)
position_x(5,13260,51)
position_x(4,13260,51)
position_x(3,13260,51)
position_x(2,13260,51)
position_x(1,13260,51)
position_x(1,13780,52)
position_x(2,13780,52)
position_x(3,13780,52)
position_x(4,13780,52)
position_x(5,13780,52)
position_x(6,0,52)
position_x(7,0,52)
position_x(8,0,52)
position_x(9,0,52)
position_x(10,0,52)
position_x(10,0,53)
position_x(9,0,53)
position_x(8,0,53)
position_x(7,0,53)
position_x(6,0,53)
position_x(5,14310,53)
position_x(4,14310,53)
position_x(3,14310,53)
position_x(2,14310,53)
position_x(1,14310,53)
position_x(1,14850,54)
position_x(2,14850,54)
position_x(3,14850,54)
position_x(4,14850,54)
position_x(5,14850,54)
position_x(6,0,54)
position_x(7,0,54)
position_x(8,0,54)
position_x(9,0,54)
position_x(10,0,54)
position_x(10,0,55)
position_x(9,0,55)
position_x(8,0,55)
position_x(7,0,55)
position_x(6,0,55)
position_x(5,15400,55)
position_x(4,15400,55)
position_x(3,15400,55)
position_x(2,15400,55)
position_x(1,15400,55)
position_x(1,15960,56)
position_x(2,15960,56)
position_x(3,15960,56)
position_x(4,15960,56)
position_x(5,15960,56)
position_x(6,0,56)
position_x(7,0,56)
position_x(8,0,56)
position_x(9,0,56)
position_x(10,0,56)
position_x(10,0,57)
position_x(9,0,57)
position_x(8,0,57)
position_x(7,0,57)
position_x(6,0,57)
position_x(5,16530,57)
position_x(4,16530,57)
position_x(3,16530,57)
position_x(2,16530,57)
position_x(1,16530,57)
position_x(1,17110,58)
position_x(2,17110,58)
position_x(3,17110,58)
position_x(4,17110,58)
position_x(5,17110,58)
position_x(6,0,58)
position_x(7,0,58)
position_x(8,0,58)
position_x(9,0,58)
position_x(10,0,58)
position_x(10,0,59)
position_x(9,0,59)
position_x(8,0,59)
position_x(7,0,59)
position_x(6,0,59)
position_x(5,17700,59)
position_x(4,17700,59)
position_x(3,17700,59)
position_x(2,17700,59)
position_x(1,17700,59)
position_x(1,18300,60)
position_x(2,18300,60)
position_x(3,18300,60)
position_x(4,18300,60)
position_x(5,18300,60)
position_x(6,0,60)
position_x(7,0,60)
position_x(8,0,60)
position_x(9,0,60)
position_x(10,0,60)
position_x(10,0,61)
position_x(9,0,61)
position_x(8,0,61)
position_x(7,0,61)
position_x(6,0,61)
position_x(5,18910,61)
position_x(4,18910,61)
position_x(3,18910,61)
position_x(2,18910,61)
position_x(1,18910,61)
position_x(1,19530,62)
position_x(2,19530,62)
position_x(3,19530,62)
position_x(4,19530,62)
position_x(5,19530,62)
position_x(6,0,62)
position_x(7,0,62)
position_x(8,0,62)
position_x(9,0,62)
position_x(10,0,62)
position_x(10,0,63)
position_x(9,0,63)
position_x(8,0,63)
position_x(7,0,63)
position_x(6,0,63)
position_x(5,20160,63)
position_x(4,20160,63)
position_x(3,20160,63)
position_x(2,20160,63)
position_x(1,20160,63)
position_x(1,20800,64)
position_x(2,20800,64)
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velocity_y(7,0,93)
velocity_y(6,0,93)
velocity_y(5,465,93)
velocity_y(4,465,93)
velocity_y(3,465,93)
velocity_y(2,465,93)
velocity_y(1,465,93)
velocity_y(1,470,94)
velocity_y(2,470,94)
velocity_y(3,470,94)
velocity_y(4,470,94)
velocity_y(5,470,94)
velocity_y(6,0,94)
velocity_y(7,0,94)
velocity_y(8,0,94)
velocity_y(9,0,94)
velocity_y(10,0,94)
velocity_y(10,0,95)
velocity_y(9,0,95)
velocity_y(8,0,95)
velocity_y(7,0,95)
velocity_y(6,0,95)
velocity_y(5,475,95)
velocity_y(4,475,95)
velocity_y(3,475,95)
velocity_y(2,475,95)
velocity_y(1,475,95)
velocity_y(1,480,96)
velocity_y(2,480,96)
velocity_y(3,480,96)
velocity_y(4,480,96)
velocity_y(5,480,96)
velocity_y(6,0,96)
velocity_y(7,0,96)
velocity_y(8,0,96)
velocity_y(9,0,96)
velocity_y(10,0,96)
velocity_y(10,0,97)
velocity_y(9,0,97)
velocity_y(8,0,97)
velocity_y(7,0,97)
velocity_y(6,0,97)
velocity_y(5,485,97)
velocity_y(4,485,97)
velocity_y(3,485,97)
velocity_y(2,485,97)
velocity_y(1,485,97)
velocity_y(1,490,98)
velocity_y(2,490,98)
velocity_y(3,490,98)
velocity_y(4,490,98)
velocity_y(5,490,98)
velocity_y(6,0,98)
velocity_y(7,0,98)
velocity_y(8,0,98)
velocity_y(9,0,98)
velocity_y(10,0,98)
velocity_y(10,0,99)
velocity_y(9,0,99)
velocity_y(8,0,99)
velocity_y(7,0,99)
velocity_y(6,0,99)
velocity_y(5,495,99)
velocity_y(4,495,99)
velocity_y(3,495,99)
velocity_y(2,495,99)
velocity_y(1,495,99)
velocity_y(1,500,100)
velocity_y(2,500,100)
velocity_y(3,500,100)
velocity_y(4,500,100)
velocity_y(5,500,100)
velocity_y(6,0,100)
velocity_y(7,0,100)
velocity_y(8,0,100)
velocity_y(9,0,100)
velocity_y(10,0,100)
velocity_y(10,0,101)
velocity_y(9,0,101)
velocity_y(8,0,101)
velocity_y(7,0,101)
velocity_y(6,0,101)
velocity_y(5,505,101)
velocity_y(4,505,101)
velocity_y(3,505,101)
velocity_y(2,505,101)
velocity_y(1,505,101)
SATISFIABLE
Models : 1
Calls : 1
Time : 0.022s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)
CPU Time : 0.022s
% Constants
mass(1). % Mass of all bodies (1 unit for simplicity)
% Define body identifiers
body(1..10).
% Initial conditions for all bodies
initial_position_x(B, 0) :- body(B).
initial_position_y(B, 0) :- body(B).
% Initial velocity for bodies 1 to 5 (those with applied forces)
initial_velocity_x(B, 0) :- body(B), B <= 5.
initial_velocity_y(B, 0) :- body(B), B <= 5.
% Initial velocity for bodies 6 to 10 (no initial velocity, static)
initial_velocity_x(B, 0) :- body(B), B > 5, 0.
initial_velocity_y(B, 0) :- body(B), B > 5, 0.
% External forces applied (only to first 5 bodies)
force_x(B, 10) :- body(B), B <= 5.
force_y(B, 5) :- body(B), B <= 5.
% No force applied to bodies 6 to 10
force_x(B, 0) :- body(B), B > 5.
force_y(B, 0) :- body(B), B > 5.
% Time steps to be considered
time(0..1).
% Calculate acceleration from force and mass (F = ma, a = F/m) for both x and y components
acceleration_x(B, Ax) :- force_x(B, Fx), mass(M), Ax = Fx / M, body(B).
acceleration_y(B, Ay) :- force_y(B, Fy), mass(M), Ay = Fy / M, body(B).
% Calculate velocity at each time step for both x and y components
velocity_x(B, Vx, T+1) :- velocity_x(B, Vx0, T), acceleration_x(B, Ax), Vx = Vx0 + Ax, time(T), body(B).
velocity_y(B, Vy, T+1) :- velocity_y(B, Vy0, T), acceleration_y(B, Ay), Vy = Vy0 + Ay, time(T), body(B).
% Initialize velocity at time 0 for both x and y components
velocity_x(B, Vx, 0) :- initial_velocity_x(B, Vx), body(B).
velocity_y(B, Vy, 0) :- initial_velocity_y(B, Vy), body(B).
% Calculate position at each time step for both x and y components
position_x(B, Px, T+1) :- position_x(B, Px0, T), velocity_x(B, Vx, T+1), Px = Px0 + Vx, time(T), body(B).
position_y(B, Py, T+1) :- position_y(B, Py0, T), velocity_y(B, Vy, T+1), Py = Py0 + Vy, time(T), body(B).
% Initialize position at time 0 for both x and y components
position_x(B, Px, 0) :- initial_position_x(B, Px), body(B).
position_y(B, Py, 0) :- initial_position_y(B, Py), body(B).
% Output the results for each body
#show position_x/3.
#show position_y/3.
#show velocity_x/3.
#show velocity_y/3.
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