使用pygame实现动量定理的小球碰撞演示动画

动量定理我们在高中的时候就已经接触过了，是十分重要的物理定理。其中的完全弹性碰撞（机械能守恒）是十分典型的例子，机械能守恒和动量定理两个公式就可以推出小球碰撞之后的速度，依据这个公式，我们就可以完成我们的动画演示了。
m 1 v 1 + m 2 v 2 = m 1 v 1 ′ + m 2 v 2 ′ m_1v_1+m_2v_2=m_1v_1'+m_2v_2' m1v1+m2v2=m1v1′+m2v2′

1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 = 1 2 m 1 v 1 ′ 2 + 1 2 m 2 v 2 ′ 2 \frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2=\frac{1}{2}m_1v_1'^2+\frac{1}{2}m_2v_2'^2 21m1v12+21m2v22=21m1v1′2+21m2v2′2
根据这两个式子，可以得出碰撞之后的 v 1 ’ v_1’ v1’和 v 2 ′ v_2' v2′的速度：
v 1 ′ = 2 m 2 m 1 + m 2 v 2 + m 1 − m 2 m 1 + m 2 v 1 v_1'=\frac{2m_2}{m_1+m_2}v_2+\frac{m_1-m_2}{m_1+m_2}v_1 v1′=m1+m22m2v2+m1+m2m1−m2v1

v 2 ′ = 2 m 1 m 1 + m 2 v 1 + m 2 − m 1 m 1 + m 2 v 2 v_2'=\frac{2m_1}{m_1+m_2}v_1+\frac{m_2-m_1}{m_1+m_2}v_2 v2′=m1+m22m1v1+m1+m2m2−m1v2

然后就可以写代码了

源代码

# color.py
# 需要用到的颜色
RED = (255,0,0)
GREEN = (0,255,0)
BLUE = (0,0,255)
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
YELLOW = (255,255,0)
UNKNOWN = (0, 255,255)

import pygame
from pygame.locals import *
from color import *# 精灵类
class ball(pygame.sprite.Sprite):def __init__(self, mass, position, velocity, color): # position 为左下角的坐标self.mass = massself.image = pygame.Surface((40, 40))self.rect = self.image.get_rect()# pygame.draw.rect(self.image, BLACK, self.rect, 1)self.image.fill(WHITE)pygame.draw.circle(self.image, color, (20, 20), 20)self.rect.bottomleft = positionself.velocity = velocity

# 主函数
import pygame, sys
from pygame.locals import *
from color import *
from ball import balldef main():pygame.init()screen = pygame.display.set_mode((800, 600))pygame.display.set_caption('动量定理动画')FPSCLOCK = pygame.time.Clock()floor1 = 200floor2 = 400floor3 = 600# 初始化小球ball1 = ball(10, (0, floor1), 10,RED)ball2 = ball(20, (760, floor1), -5,BLACK)ball3 = ball(10, (0, floor2), 10,GREEN)ball4 = ball(10, (760, floor2), -10,BLUE)ball5 = ball(1, (0, floor3), 10, YELLOW)ball6 = ball(1000000000000000000000, (400, floor3), 0, UNKNOWN)# 绘制两个小球screen.fill(WHITE)pygame.draw.line(screen, BLACK,(0, floor1), (800, floor1), 1)pygame.draw.line(screen, BLACK,(0, floor2), (800, floor2), 1)pygame.draw.line(screen, BLACK,(0, floor3), (800, floor3), 1)screen.blit(ball1.image, ball1.rect)screen.blit(ball2.image, ball2.rect)screen.blit(ball3.image, ball3.rect)screen.blit(ball4.image, ball4.rect)screen.blit(ball5.image, ball5.rect)screen.blit(ball6.image, ball6.rect)while True:for event in pygame.event.get():if event.type == QUIT:pygame.quit()sys.exit()if collision_check(ball1.rect, ball2.rect):v1 = ball1.velocityv2 = ball2.velocitym1 = ball1.massm2 = ball2.massball1.velocity = int(2*m2*v2/(m1+m2)+((m1-m2)/(m1+m2))*v1)ball2.velocity = int(2*m1*v1/(m1+m2)+((m2-m1)/(m1+m2))*v2)if ball3.rect.right > ball4.rect.left and ball3.rect.right - ball3.velocity <= ball4.rect.left - ball4.velocity:v1 = ball3.velocityv2 = ball4.velocitym1 = ball3.massm2 = ball4.massball3.velocity = int(2*m2*v2/(m1+m2)+((m1-m2)/(m1+m2))*v1)ball4.velocity = int(2*m1*v1/(m1+m2)+((m2-m1)/(m1+m2))*v2)if ball5.rect.right > ball6.rect.left and ball5.rect.right - ball5.velocity <= ball6.rect.left - ball6.velocity:v1 = ball5.velocityv2 = ball6.velocitym1 = ball5.massm2 = ball6.massprint(ball5.velocity)ball5.velocity = int(2*m2*v2/(m1+m2)+((m1-m2)/(m1+m2))*v1)ball6.velocity = int(2*m1*v1/(m1+m2)+((m2-m1)/(m1+m2))*v2)if ball1.rect.left < 0 or ball1.rect.right > 800:ball1.velocity = -ball1.velocityif (ball1.rect.left < 0 and ball1.velocity < 0) or (ball1.rect.right > 800 and ball1.velocity > 0):ball1.velocity = -ball1.velocityif ball2.rect.left < 0 or ball2.rect.right > 800:ball2.velocity = -ball2.velocityif (ball2.rect.left < 0 and ball2.velocity < 0) or (ball2.rect.right > 800 and ball2.velocity > 0):ball2.velocity = -ball2.velocityif ball3.rect.left < 0 or ball3.rect.right > 800:ball3.velocity = -ball3.velocityif (ball3.rect.left < 0 and ball3.velocity < 0) or (ball3.rect.right > 800 and ball3.velocity > 0):ball3.velocity = -ball3.velocityif ball4.rect.left < 0 or ball4.rect.right > 800:ball4.velocity = -ball4.velocityif (ball4.rect.left < 0 and ball4.velocity < 0) or (ball4.rect.right > 800 and ball4.velocity > 0):ball4.velocity = -ball4.velocityif ball5.rect.left < 0 or ball5.rect.right > 800:ball5.velocity = -ball5.velocityif (ball5.rect.left < 0 and ball5.velocity < 0) or (ball5.rect.right > 800 and ball5.velocity > 0):ball5.velocity = -ball5.velocityif ball6.rect.left < 0 or ball6.rect.right > 800:ball6.velocity = -ball6.velocityif (ball6.rect.left < 0 and ball6.velocity < 0) or (ball6.rect.right > 800 and ball6.velocity > 0):ball6.velocity = -ball6.velocityball1.rect.left += ball1.velocityball2.rect.left += ball2.velocityball3.rect.left += ball3.velocityball4.rect.left += ball4.velocityball5.rect.left += ball5.velocityball6.rect.left += ball6.velocityscreen.fill(WHITE)pygame.draw.line(screen, BLACK,(0, floor1), (800, floor1), 1)pygame.draw.line(screen, BLACK,(0, floor2), (800, floor2), 1)pygame.draw.line(screen, BLACK,(0, floor3), (800, floor3), 1)screen.blit(ball1.image, ball1.rect)screen.blit(ball2.image, ball2.rect)screen.blit(ball3.image, ball3.rect)screen.blit(ball4.image, ball4.rect)screen.blit(ball5.image, ball5.rect)screen.blit(ball6.image, ball6.rect)pygame.display.update()FPSCLOCK.tick(60)if __name__ == '__main__':main()

效果

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pygame动画演示小球碰撞

使用pygame实现动量定理的小球碰撞演示动画

源代码

效果

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