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ss17:viele_dinge_fliegen_im_weltall_durcheinander:testprogramme
Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen gezeigt.
| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
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ss17:viele_dinge_fliegen_im_weltall_durcheinander:testprogramme [2017/08/23 21:55] mtoppermann [Testprogramme] |
ss17:viele_dinge_fliegen_im_weltall_durcheinander:testprogramme [2017/08/28 15:41] (aktuell) mtoppermann [Vergleich von Planetenbewegungen mit verschiedenen Methoden] |
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| Zeile 4: | Zeile 4: | ||
| ===== Vergleich von Planetenbewegungen mit verschiedenen Methoden===== | ===== Vergleich von Planetenbewegungen mit verschiedenen Methoden===== | ||
| + | |||
| + | In diesem Skript wird die Genauigkeit des Euler-Verfahrens mit dem Leapfrog-Verfahren am Bespiel der Erdbewegung | ||
| + | um die Sonne verglichen. Die Bewegung der dunkelblauen Erde wir durch das Leapfrog-Verfahren berechnet, das der hellblauen durch das Euler-Verfahren. Nach einiger Zeit sieht man bereits deutliche Unterschiede in der Bahnbewegung: Die dunkelblaue Erde verlässt die richtige Bahn langsamer, da ihre die Berechnungsfehler kleiner sind. | ||
| <code python> | <code python> | ||
| from functions import * | from functions import * | ||
| import pygame | import pygame | ||
| + | |||
| class Sun(object): | class Sun(object): | ||
| - | """Our Sun in the point of origin | + | |
| - | """ | + | |
| def __init__(self): | def __init__(self): | ||
| + | """initialize all necessary properties of the sun | ||
| + | """ | ||
| self.x = 0 | self.x = 0 | ||
| self.y = 0 | self.y = 0 | ||
| self.radius = 20 | self.radius = 20 | ||
| self.mass = 1.989e30 | self.mass = 1.989e30 | ||
| - | self.colour = (255,255,0) | + | self.colour = (255, 255, 0) |
| + | |||
| class Earth(object): | class Earth(object): | ||
| - | """Our home | + | |
| - | """ | + | def __init__(self, color): |
| - | def __init__(self,color): | + | """initialize all necessary properties of the earth |
| + | """ | ||
| self.x = 1.49e11 | self.x = 1.49e11 | ||
| self.y = 0. | self.y = 0. | ||
| self.radius = 10 | self.radius = 10 | ||
| self.mass = 5.97e24 | self.mass = 5.97e24 | ||
| - | self.velocity = np.array([0.,2.978e4]) | + | self.velocity = np.array([0., 2.978e4]) |
| - | self.force = np.array([0,0]) | + | self.force = np.array([0, 0]) |
| self.colour = (color) | self.colour = (color) | ||
| - | self.positions = [(int(self.x * 1e-9 + width/2), | + | |
| - | int(self.y * 1e-9 + height/2))] | + | |
| - | + | ||
| - | # leapfrog method for DE-solving | + | |
| def move(self): | def move(self): | ||
| + | """leapfrog method for differential-equation-solving | ||
| + | """ | ||
| self.x += 0.5 * self.velocity[0] * dt | self.x += 0.5 * self.velocity[0] * dt | ||
| self.y += 0.5 * self.velocity[1] * dt | self.y += 0.5 * self.velocity[1] * dt | ||
| Zeile 40: | Zeile 44: | ||
| self.x += 0.5 * self.velocity[0] * dt | self.x += 0.5 * self.velocity[0] * dt | ||
| self.y += 0.5 * self.velocity[1] * dt | self.y += 0.5 * self.velocity[1] * dt | ||
| - | + | ||
| - | # euler method for DE-solving | + | |
| def move2(self): | def move2(self): | ||
| + | """euler-method for differential-equation-solving | ||
| + | """ | ||
| self.x += self.velocity[0] * dt | self.x += self.velocity[0] * dt | ||
| self.y += self.velocity[1] * dt | self.y += self.velocity[1] * dt | ||
| self.velocity += self.force/self.mass * dt | self.velocity += self.force/self.mass * dt | ||
| + | |||
| def draw(a, points): | def draw(a, points): | ||
| - | """Draws an object and its trail on the screen | + | """Draws an object on the screen |
| """ | """ | ||
| pygame.draw.circle(screen, a.colour, (int(a.x * 10e-10) + width/2, | pygame.draw.circle(screen, a.colour, (int(a.x * 10e-10) + width/2, | ||
| int(a.y * 10e-10) + height/2), a.radius, 0) | int(a.y * 10e-10) + height/2), a.radius, 0) | ||
| pygame.draw.aalines(screen, a.colour, False, points, 2) | pygame.draw.aalines(screen, a.colour, False, points, 2) | ||
| + | |||
| def draw2(a): | def draw2(a): | ||
| """Draws an object in the middle of the screen | """Draws an object in the middle of the screen | ||
| """ | """ | ||
| pygame.draw.circle(screen, a.colour, (width/2, height/2), a.radius, 0) | pygame.draw.circle(screen, a.colour, (width/2, height/2), a.radius, 0) | ||
| - | + | ||
| - | def last_elems(elems, k): | + | |
| - | """Returns the last k elements of a list | + | |
| - | """ | + | |
| - | tmp = [] | + | |
| - | for i in xrange(k): | + | |
| - | if i > len(elems): | + | |
| - | break | + | |
| - | elif i < len(elems): | + | |
| - | tmp.append(elems[-(i+1)]) | + | |
| - | return tmp | + | |
| dt = 36000 | dt = 36000 | ||
| - | (width, height) = (1000,600) | + | (width, height) = (1000, 600) |
| screen = pygame.display.set_mode((width, height)) | screen = pygame.display.set_mode((width, height)) | ||
| pygame.display.set_caption(" ") | pygame.display.set_caption(" ") | ||
| - | background_colour = (10,10,10) | + | bgcolour = (10, 10, 10) |
| - | + | ||
| - | earth = Earth((0,0,255)) | + | earth = Earth((0, 0, 255)) |
| - | kerbin = Earth((50,150,255)) | + | kerbin = Earth((50, 150, 255)) |
| - | sonne = Sun() | + | sun = Sun() |
| - | + | ||
| - | count = 0 | + | |
| running = True | running = True | ||
| while running: | while running: | ||
| Zeile 86: | Zeile 79: | ||
| if event.type == pygame.QUIT: | if event.type == pygame.QUIT: | ||
| running = False | running = False | ||
| - | + | ||
| - | #every ten steps, the trail is updated | + | |
| - | if count % 10 == 0: | + | |
| - | erde.positions.append((int(1e-9 * erde.x) + width/2, | + | |
| - | int(1e-9 * erde.y) + height/2)) | + | |
| - | kerbin.positions.append((int(1e-9 * kerbin.x) + width/2, | + | |
| - | int(1e-9 * kerbin.y) + height/2)) | + | |
| - | linepoints1 = last_elems(erde.positions, 200) | + | |
| - | linepoints2 = last_elems(kerbin.positions, 200) | + | |
| # display everything | # display everything | ||
| - | screen.fill(background_colour) | + | screen.fill(bgcolour) |
| draw(erde, linepoints1) | draw(erde, linepoints1) | ||
| draw(kerbin, linepoints2) | draw(kerbin, linepoints2) | ||
| draw2(sonne) | draw2(sonne) | ||
| pygame.display.update() | pygame.display.update() | ||
| + | |||
| # calculate everything | # calculate everything | ||
| - | erde.force = get_force(erde, sonne) | + | erde.force = get_force(earth, sun) |
| - | kerbin.force = get_force(kerbin, sonne) | + | kerbin.force = get_force(kerbin, sun) |
| erde.move() | erde.move() | ||
| kerbin.move2() | kerbin.move2() | ||
| - | + | ||
| - | count += 1 | + | |
| </code> | </code> | ||
| - | |||
| =====Euler-Verfahren vs Verlet(Leapfrog)-Verfahren===== | =====Euler-Verfahren vs Verlet(Leapfrog)-Verfahren===== | ||
ss17/viele_dinge_fliegen_im_weltall_durcheinander/testprogramme.1503518107.txt.gz · Zuletzt geändert: 2017/08/23 21:55 von mtoppermann
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