fixed acc vs force typo

Author: liminchen

0_getting_started/simulator0.py

@@ -5,11 +5,10 @@
 import pygame       # for visualization
 
 # simulation setup
-m = 1000                    # mass of particle
 x = np.array([0.0, 0.0])    # position of particle
-v = np.array([0.1, 0.1])    # velocity of particle
-g = np.array([0, -9.81])    # gravitational acceleration
-h = 0.1                     # time step size in seconds
+v = np.array([0.0, 0.0])    # velocity of particle
+g = np.array([0.0, -10.0])  # gravitational acceleration
+h = 0.01                # time step size in seconds
 
 # visualization/rendering setup
 pygame.init()
@@ -41,7 +40,7 @@ def screen_projection(x):           # convert simulated coordinates to window co
         pygame.time.wait(int(1000.0 / render_FPS))  # wait to render the next frame
 
     # step forward the simulation by updating particle velocity and position
-    v += h * g / m
+    v += h * g
     x += h * v
 
     # pause the simulation when the particle touches on the ground 

0_getting_started/simulator1.py

@@ -6,12 +6,12 @@
 
 # simulation setup
 m = 1000                    # mass of particle
-x = np.array([0.1, 0.0])    # position of particle
+x = np.array([0.3, 0.0])    # position of particle
 v = np.array([0.0, 0.0])    # velocity of particle
-g = np.array([0, -9.81])    # gravitational acceleration
+g = np.array([0.0, -10.0])  # gravitational acceleration
 spring_rest_len = 0.3       # rest length of the spring ###
-spring_stiffness = 1000     # stiffness of the spring ###
-h = 0.1                     # time step size in seconds
+spring_stiffness = 1e5      # stiffness of the spring ###
+h = 0.01                    # time step size in seconds
 
 # visualization/rendering setup
 pygame.init()
@@ -34,10 +34,9 @@ def screen_projection(x):           # convert simulated coordinates to window co
     # update the frame to display according to render_FPS
     if time_step % int(math.ceil((1.0 / render_FPS) / h)) == 0:
         # fill the background with white color, display simulation time at the top,
-        # render a floor at y=-1, draw the spring segment, and render the particle as a circle:
+        # draw the spring segment, and render the particle as a circle:
         screen.fill((255, 255, 255))    
         pygame.display.set_caption('Current time: ' + f'{time_step * h: .2f}s')
-        pygame.draw.aaline(screen, (0, 0, 255), screen_projection([-2, -1]), screen_projection([2, -1]))
         pygame.draw.aaline(screen, (0, 0, 255), screen_projection([0, 0]), screen_projection(x)) ###
         pygame.draw.circle(screen, (0, 0, 255), screen_projection(x), 0.1 * scale)
         pygame.display.flip()   # flip the display
@@ -47,12 +46,7 @@ def screen_projection(x):           # convert simulated coordinates to window co
     spring_cur_len = math.sqrt(x[0] * x[0] + x[1] * x[1]) ###
     spring_displacement = spring_cur_len - spring_rest_len ###
     spring_force = -spring_stiffness * spring_displacement * (x / spring_cur_len) ###
-    v += h * (g + spring_force) / m
+    v += h * (g + spring_force / m)
     x += h * v
 
-    # pause the simulation when the particle touches on the ground 
-    if x[1] <= -1:
-        input()
-        break
-
     time_step += 1  # update time step counter

0_getting_started/simulator2.py

@@ -11,13 +11,13 @@
 n_seg = 4                   # number of springs per side of the square
 [x, e] = square_mesh.generate(side_length, n_seg)   # array of particle positions and springs   ###
 v = np.array([[0.0, 0.0]] * len(x))     # velocity array of particles ###
-g = np.array([0, -9.81])    # gravitational acceleration
+g = np.array([0.0, -10.0])  # gravitational acceleration
 spring_rest_len = []        # rest length array of the springs ###
 for i in range(0, len(e)):  # calculate the rest length of each spring
     spring_vec = x[e[i][0]] - x[e[i][1]]    # the vector connecting two ends of spring i
     spring_rest_len.append(math.sqrt(spring_vec[0] * spring_vec[0] + spring_vec[1] * spring_vec[1]))
-spring_stiffness = 1000     # stiffness of the spring
-h = 0.1                     # time step size in seconds
+spring_stiffness = 1e6      # stiffness of the spring
+h = 0.01                    # time step size in seconds
 
 # visualization/rendering setup
 pygame.init()
@@ -58,8 +58,8 @@ def screen_projection(x):           # convert simulated coordinates to window co
         spring_displacement = spring_cur_len - spring_rest_len[i]
         spring_force = -spring_stiffness * spring_displacement * (spring_vec / spring_cur_len)
         # update the velocity of the two ends of spring i
-        v[e[i][0]] += h * (g + spring_force) / m
-        v[e[i][1]] += h * (g - spring_force) / m
+        v[e[i][0]] += h * (g + spring_force / m)
+        v[e[i][1]] += h * (g - spring_force / m)
     # fix the top left and top right corner by setting velocity to 0:
     v[n_seg] = v[(n_seg + 1) * (n_seg + 1) - 1] = np.array([0, 0])
     # update the position of each particle: