如何调整我的篮球-FT（罚球）模拟以找到关节上的必要扭矩
How to adjust my basketball-FT(Free throw) simulation to find the necessary torque(s) on joints
我正在模拟以 angular 运动开始并进入抛射运动的篮球投掷。 Physics set-up of simulation
我的目标是深入了解投掷篮球时施加在关节（如肘部和肩部）上的扭矩大小。在我的模拟中，扭矩和释放角度是输入，轨迹是输出。我想 'tweek' 输入以获得挥动球网的球轨迹（得分）。
现在我将它缩小到肘关节，所以基本上是一个弹射器，如下面的代码所示，而且篮子还没有在里面。
但在此扩展之前，我想 运行 模拟多个 'release angles' 和不同的 'torques on elbow'。
如您所见，我试图在第 11 行和第 17 行（已注释掉）中制作一个包含扭矩和释放角度的附加列表，并且我想添加另一个循环，以便整个模拟将 运行 具有不同的角度 [re_angl_deg] 列表和扭矩 [torq_elb] 列表作为输入。
不幸的是，这并没有真正奏效。
现在我的问题是：是否有其他方法可以让模拟 运行 多次，每次都有不同的角度和扭矩（就像我制作的列表一样）。
希望有人能给我一些建议！ Regards.TF
import numpy as np
import matplotlib.pyplot as plt
import math
# Define settings.
endTime = 60 # The time (seconds) that we simulate.
dt = 0.001 # The time step (seconds) that we use in the discretization.
w0 = 0 # The initial velocity [m/s].
tet0 = 15 # The initial position [m].
torq_elb = 70 #[Nm]
#torq_elb = np.array([50,55,60,65,70,75,80,85,90,95,100]) #[Nm]
I = 0.16 #[kgm^2] inertia
x_pos = 0 #initial x position
y_pos = 0 # initial y Position
r = 0.3 # lower arm length [m]
re_angl_deg = 50 # release angle degrees
#re_angl_deg = np.array([30,32,34,36,38,40,42,44,45,47,49,50,52,54])
re_angl_rad = math.radians(re_angl_deg)
g = 9.81 # The gravitational acceleration [m/s^2].
m_ball = 0.6 # The mass of the ball [kg].
rho_air = 1.2041 #[kg/m3]
c_drag = 0.3 # drag coefficient
area_b = (4*math.pi*r**2)/2 # surface area of the ball
# Set up variables.
time = np.arange(0, endTime + dt, dt) # A list with all times we want to plot at.
w = np.zeros(len(time)) # A list for the angular velocity. [rad/s]
w_deg = np.zeros(len(time)) # list for angle of angular velocity
tet = np.zeros(len(time)) # A list for the distance.
x_pos = np.zeros(len(time)) # A list for the xpos
y_pos = np.zeros(len(time)) # A list for the ypos.
x_pos_released = np.zeros(len(time)) # A list for the xpos when released
y_pos_released = np.zeros(len(time)) # A list for the ypos when released
v_x = np.zeros(len(time)) # A list for the xpos
v_y = np.zeros(len(time)) # A list for the ypos.
v_t = np.zeros(len(time)) # List for tangent speed
v_ang = np.zeros(len(time)) # list for angle of the tangent speed
air_res = np.zeros(len(time)) # list for total air resistance
air_res_x = np.zeros(len(time)) # list for X vector of air resistance
air_res_y = np.zeros(len(time)) # list for Y vector of air resistance
w[0] = w0 #start w
tet[0] = math.radians(tet0)
x_pos[0] = 0 # xpos start
y_pos[0] = 1.8 # approximate hight of a person that is throwing
released=False
# Run simulation.
for i in range(1, len(time)):
if (released==False):
w[i] = w[i-1] + torq_elb / I *dt
tet[i] = tet[i-1] + w[i] * dt
x_pos[i] = x_pos[i-1] + r * math.cos(w[i] - w[i-1]) * dt
y_pos[i] = y_pos[i-1] + r * math.sin(w[i] - w[i-1]) * dt
if (tet[i] > re_angl_rad) and (released==False):
v_release = w[i] * r
tet_release = tet[i]
v_x[i-1] = v_release * math.cos(tet_release)
v_y[i-1] = v_release * math.sin(tet_release)
x_pos_released[i-1]=x_pos[i]
y_pos_released[i-1]=y_pos[i]
released=True
w[i] = 0
if (released==True):
v_x[i]=v_x[i-1]
v_y[i]=v_y[i-1]
v_t[i] = math.sqrt(v_x[i-1]**2+v_y[i-1]**2)
v_ang[i] = math.atan(v_y[i-1]/v_x[i-1])
air_res[i] = 0.5*rho_air*v_t[i]**2*c_drag*area_b ##Force airresitance
air_res_x[i] = (air_res[i] * math.cos(v_ang[i]))/m_ball
air_res_y[i] = (air_res[i] * math.sin(v_ang[i]))/m_ball
v_x[i]= v_x[i-1] - air_res_x[i] * dt
v_y[i]= v_y[i-1] - (g + air_res_y[i]) * dt
x_pos_released[i] = x_pos_released[i-1] + ((v_x[i-1] + v_x[i])/2) * dt
y_pos_released[i] = y_pos_released[i-1] + ((v_y[i-1] + v_y[i])/2) * dt
# Display results.
plt.plot(time, tet, color='pink',label='Angular Displacement')
plt.plot(time, w, color='yellow', label='Angular Velocity')
plt.plot(time, y_pos_released,color='blue',label='Y_position')
plt.plot(time, x_pos_released,color='purple',label='X_position')
plt.plot(time, v_t, color='black',label='Tangent Velocity')
plt.plot(time, air_res, color='cyan',label='Force Air_res')
plt.xlabel('Time [s]')
plt.ylabel('YYYY')
plt.legend()
plt.xlim(0,1)
plt.ylim(0,10)
plt.show()
plt.plot(x_pos_released,y_pos_released,':',color='green' ,label='Trajectory ball')
plt.xlabel('Distance[m]')
plt.ylabel('Height[m]')
plt.xlim(0,4)
plt.ylim(0,4)
plt.legend()
plt.show()
我可能会将每个模拟的值存储在字典中，这样您就可以将其写入文件，然后只需调用特定的释放角度和扭矩即可显示，而不是尝试绘制每个模拟值。但是你只需要在这里计算出嵌套循环的逻辑。
然后您可以遍历结果以获取图表，或者将其保留为输入，以便您可以调用特定的组合来输出。您需要 pip install choice 来实施我的解决方案的输入部分。
代码:
import numpy as np
import matplotlib.pyplot as plt
import math
# Define settings.
endTime = 60 # The time (seconds) that we simulate.
dt = 0.001 # The time step (seconds) that we use in the discretization.
w0 = 0 # The initial velocity [m/s].
tet0 = 15 # The initial position [m].
#torq_elb = 70 #[Nm]
torq_elb_list = np.array([50,55,60,65,70,75,80,85,90,95,100]) #[Nm]
I = 0.16 #[kgm^2] inertia
x_pos = 0 #initial x position
y_pos = 0 # initial y Position
r = 0.3 # lower arm length [m]
#re_angl_deg = 50 # release angle degrees
re_angl_deg_list = np.array([30,32,34,36,38,40,42,44,45,47,49,50,52,54])
g = 9.81 # The gravitational acceleration [m/s^2].
m_ball = 0.6 # The mass of the ball [kg].
rho_air = 1.2041 #[kg/m3]
c_drag = 0.3 # drag coefficient
area_b = (4*math.pi*r**2)/2 # surface area of the ball
results = {}
count = 1
tot = len(torq_elb_list) * len(re_angl_deg_list)
for torq_elb in torq_elb_list:
for re_angl_deg in re_angl_deg_list:
results[(torq_elb, re_angl_deg)] = {}
re_angl_rad = math.radians(re_angl_deg )
# Set up variables.
time = np.arange(0, endTime + dt, dt) # A list with all times we want to plot at.
w = np.zeros(len(time)) # A list for the angular velocity. [rad/s]
w_deg = np.zeros(len(time)) # list for angle of angular velocity
tet = np.zeros(len(time)) # A list for the distance.
x_pos = np.zeros(len(time)) # A list for the xpos
y_pos = np.zeros(len(time)) # A list for the ypos.
x_pos_released = np.zeros(len(time)) # A list for the xpos when released
y_pos_released = np.zeros(len(time)) # A list for the ypos when released
v_x = np.zeros(len(time)) # A list for the xpos
v_y = np.zeros(len(time)) # A list for the ypos.
v_t = np.zeros(len(time)) # List for tangent speed
v_ang = np.zeros(len(time)) # list for angle of the tangent speed
air_res = np.zeros(len(time)) # list for total air resistance
air_res_x = np.zeros(len(time)) # list for X vector of air resistance
air_res_y = np.zeros(len(time)) # list for Y vector of air resistance
w[0] = w0 #start w
tet[0] = math.radians(tet0)
x_pos[0] = 0 # xpos start
y_pos[0] = 1.8 # approximate hight of a person that is throwing
released=False
# Run simulation.
for i in range(1, len(time)):
if (released==False):
w[i] = w[i-1] + torq_elb / I *dt
tet[i] = tet[i-1] + w[i] * dt
x_pos[i] = x_pos[i-1] + r * math.cos(w[i] - w[i-1]) * dt
y_pos[i] = y_pos[i-1] + r * math.sin(w[i] - w[i-1]) * dt
if (tet[i] > re_angl_rad) and (released==False):
v_release = w[i] * r
tet_release = tet[i]
v_x[i-1] = v_release * math.cos(tet_release)
v_y[i-1] = v_release * math.sin(tet_release)
x_pos_released[i-1]=x_pos[i]
y_pos_released[i-1]=y_pos[i]
released=True
w[i] = 0
if (released==True):
v_x[i]=v_x[i-1]
v_y[i]=v_y[i-1]
v_t[i] = math.sqrt(v_x[i-1]**2+v_y[i-1]**2)
v_ang[i] = math.atan(v_y[i-1]/v_x[i-1])
air_res[i] = 0.5*rho_air*v_t[i]**2*c_drag*area_b ##Force airresitance
air_res_x[i] = (air_res[i] * math.cos(v_ang[i]))/m_ball
air_res_y[i] = (air_res[i] * math.sin(v_ang[i]))/m_ball
v_x[i]= v_x[i-1] - air_res_x[i] * dt
v_y[i]= v_y[i-1] - (g + air_res_y[i]) * dt
x_pos_released[i] = x_pos_released[i-1] + ((v_x[i-1] + v_x[i])/2) * dt
y_pos_released[i] = y_pos_released[i-1] + ((v_y[i-1] + v_y[i])/2) * dt
# Store simulation results
results[(torq_elb, re_angl_deg)]['time'] = time
results[(torq_elb, re_angl_deg)]['tet'] = tet
results[(torq_elb, re_angl_deg)]['w'] = w
results[(torq_elb, re_angl_deg)]['y_pos_released'] = y_pos_released
results[(torq_elb, re_angl_deg)]['x_pos_released'] = x_pos_released
results[(torq_elb, re_angl_deg)]['v_t'] = v_t
results[(torq_elb, re_angl_deg)]['air_res'] = air_res
print(f'Finished simulation: torque: {torq_elb} release: {re_angl_deg}\t{count} of {tot}')
count+=1
# Display results for a particular (torq, re_angl_deg).
#pip install choice
import choice
print('Choose torque.')
torque_choice = int(choice.Menu([str(x) for x in torq_elb_list.tolist()]).ask())
print('Choose release degree.')
release_choice = int(choice.Menu([str(x) for x in re_angl_deg_list.tolist()]).ask())
time = results[(torque_choice, release_choice)]['time']
tet = results[(torque_choice, release_choice)]['tet']
w = results[(torque_choice, release_choice)]['w']
y_pos_released = results[(torque_choice, release_choice)]['y_pos_released']
x_pos_released = results[(torque_choice, release_choice)]['x_pos_released']
v_t = results[(torque_choice, release_choice)]['v_t']
air_res = results[(torque_choice, release_choice)]['air_res']
plt.plot(time, tet, color='pink',label='Angular Displacement')
plt.plot(time, w, color='yellow', label='Angular Velocity')
plt.plot(time, y_pos_released,color='blue',label='Y_position')
plt.plot(time, x_pos_released,color='purple',label='X_position')
plt.plot(time, v_t, color='black',label='Tangent Velocity')
plt.plot(time, air_res, color='cyan',label='Force Air_res')
plt.xlabel('Time [s]')
plt.ylabel('YYYY')
plt.title('Torque: %s - Release: %s°' %(torque_choice,release_choice))
plt.legend()
plt.xlim(0,1)
plt.ylim(0,10)
plt.show()
plt.plot(x_pos_released,y_pos_released,':',color='green' ,label='Trajectory ball')
plt.xlabel('Distance[m]')
plt.ylabel('Height[m]')
plt.title('Torque: %s - Release: %s°' %(torque_choice,release_choice))
plt.xlim(0,4)
plt.ylim(0,4)
plt.legend()
plt.show()
输入：
Choose torque.
Make a choice:
0: 50
1: 55
2: 60
3: 65
4: 70
5: 75
6: 80
7: 85
8: 90
9: 95
Enter number or name; return for next page
? 0
Choose release degree.
Make a choice:
0: 30
1: 32
2: 34
3: 36
4: 38
5: 40
6: 42
7: 44
8: 45
9: 47
Enter number or name; return for next page
? 4
输出：
我正在模拟以 angular 运动开始并进入抛射运动的篮球投掷。 Physics set-up of simulation
我的目标是深入了解投掷篮球时施加在关节（如肘部和肩部）上的扭矩大小。在我的模拟中，扭矩和释放角度是输入，轨迹是输出。我想 'tweek' 输入以获得挥动球网的球轨迹（得分）。 现在我将它缩小到肘关节，所以基本上是一个弹射器，如下面的代码所示，而且篮子还没有在里面。
但在此扩展之前，我想 运行 模拟多个 'release angles' 和不同的 'torques on elbow'。 如您所见，我试图在第 11 行和第 17 行（已注释掉）中制作一个包含扭矩和释放角度的附加列表，并且我想添加另一个循环，以便整个模拟将 运行 具有不同的角度 [re_angl_deg] 列表和扭矩 [torq_elb] 列表作为输入。 不幸的是，这并没有真正奏效。 现在我的问题是：是否有其他方法可以让模拟 运行 多次，每次都有不同的角度和扭矩（就像我制作的列表一样）。
希望有人能给我一些建议！ Regards.TF
import numpy as np
import matplotlib.pyplot as plt
import math
# Define settings.
endTime = 60 # The time (seconds) that we simulate.
dt = 0.001 # The time step (seconds) that we use in the discretization.
w0 = 0 # The initial velocity [m/s].
tet0 = 15 # The initial position [m].
torq_elb = 70 #[Nm]
#torq_elb = np.array([50,55,60,65,70,75,80,85,90,95,100]) #[Nm]
I = 0.16 #[kgm^2] inertia
x_pos = 0 #initial x position
y_pos = 0 # initial y Position
r = 0.3 # lower arm length [m]
re_angl_deg = 50 # release angle degrees
#re_angl_deg = np.array([30,32,34,36,38,40,42,44,45,47,49,50,52,54])
re_angl_rad = math.radians(re_angl_deg)
g = 9.81 # The gravitational acceleration [m/s^2].
m_ball = 0.6 # The mass of the ball [kg].
rho_air = 1.2041 #[kg/m3]
c_drag = 0.3 # drag coefficient
area_b = (4*math.pi*r**2)/2 # surface area of the ball
# Set up variables.
time = np.arange(0, endTime + dt, dt) # A list with all times we want to plot at.
w = np.zeros(len(time)) # A list for the angular velocity. [rad/s]
w_deg = np.zeros(len(time)) # list for angle of angular velocity
tet = np.zeros(len(time)) # A list for the distance.
x_pos = np.zeros(len(time)) # A list for the xpos
y_pos = np.zeros(len(time)) # A list for the ypos.
x_pos_released = np.zeros(len(time)) # A list for the xpos when released
y_pos_released = np.zeros(len(time)) # A list for the ypos when released
v_x = np.zeros(len(time)) # A list for the xpos
v_y = np.zeros(len(time)) # A list for the ypos.
v_t = np.zeros(len(time)) # List for tangent speed
v_ang = np.zeros(len(time)) # list for angle of the tangent speed
air_res = np.zeros(len(time)) # list for total air resistance
air_res_x = np.zeros(len(time)) # list for X vector of air resistance
air_res_y = np.zeros(len(time)) # list for Y vector of air resistance
w[0] = w0 #start w
tet[0] = math.radians(tet0)
x_pos[0] = 0 # xpos start
y_pos[0] = 1.8 # approximate hight of a person that is throwing
released=False
# Run simulation.
for i in range(1, len(time)):
if (released==False):
w[i] = w[i-1] + torq_elb / I *dt
tet[i] = tet[i-1] + w[i] * dt
x_pos[i] = x_pos[i-1] + r * math.cos(w[i] - w[i-1]) * dt
y_pos[i] = y_pos[i-1] + r * math.sin(w[i] - w[i-1]) * dt
if (tet[i] > re_angl_rad) and (released==False):
v_release = w[i] * r
tet_release = tet[i]
v_x[i-1] = v_release * math.cos(tet_release)
v_y[i-1] = v_release * math.sin(tet_release)
x_pos_released[i-1]=x_pos[i]
y_pos_released[i-1]=y_pos[i]
released=True
w[i] = 0
if (released==True):
v_x[i]=v_x[i-1]
v_y[i]=v_y[i-1]
v_t[i] = math.sqrt(v_x[i-1]**2+v_y[i-1]**2)
v_ang[i] = math.atan(v_y[i-1]/v_x[i-1])
air_res[i] = 0.5*rho_air*v_t[i]**2*c_drag*area_b ##Force airresitance
air_res_x[i] = (air_res[i] * math.cos(v_ang[i]))/m_ball
air_res_y[i] = (air_res[i] * math.sin(v_ang[i]))/m_ball
v_x[i]= v_x[i-1] - air_res_x[i] * dt
v_y[i]= v_y[i-1] - (g + air_res_y[i]) * dt
x_pos_released[i] = x_pos_released[i-1] + ((v_x[i-1] + v_x[i])/2) * dt
y_pos_released[i] = y_pos_released[i-1] + ((v_y[i-1] + v_y[i])/2) * dt
# Display results.
plt.plot(time, tet, color='pink',label='Angular Displacement')
plt.plot(time, w, color='yellow', label='Angular Velocity')
plt.plot(time, y_pos_released,color='blue',label='Y_position')
plt.plot(time, x_pos_released,color='purple',label='X_position')
plt.plot(time, v_t, color='black',label='Tangent Velocity')
plt.plot(time, air_res, color='cyan',label='Force Air_res')
plt.xlabel('Time [s]')
plt.ylabel('YYYY')
plt.legend()
plt.xlim(0,1)
plt.ylim(0,10)
plt.show()
plt.plot(x_pos_released,y_pos_released,':',color='green' ,label='Trajectory ball')
plt.xlabel('Distance[m]')
plt.ylabel('Height[m]')
plt.xlim(0,4)
plt.ylim(0,4)
plt.legend()
plt.show()
我可能会将每个模拟的值存储在字典中，这样您就可以将其写入文件，然后只需调用特定的释放角度和扭矩即可显示，而不是尝试绘制每个模拟值。但是你只需要在这里计算出嵌套循环的逻辑。
然后您可以遍历结果以获取图表，或者将其保留为输入，以便您可以调用特定的组合来输出。您需要 pip install choice 来实施我的解决方案的输入部分。
代码:
import numpy as np
import matplotlib.pyplot as plt
import math
# Define settings.
endTime = 60 # The time (seconds) that we simulate.
dt = 0.001 # The time step (seconds) that we use in the discretization.
w0 = 0 # The initial velocity [m/s].
tet0 = 15 # The initial position [m].
#torq_elb = 70 #[Nm]
torq_elb_list = np.array([50,55,60,65,70,75,80,85,90,95,100]) #[Nm]
I = 0.16 #[kgm^2] inertia
x_pos = 0 #initial x position
y_pos = 0 # initial y Position
r = 0.3 # lower arm length [m]
#re_angl_deg = 50 # release angle degrees
re_angl_deg_list = np.array([30,32,34,36,38,40,42,44,45,47,49,50,52,54])
g = 9.81 # The gravitational acceleration [m/s^2].
m_ball = 0.6 # The mass of the ball [kg].
rho_air = 1.2041 #[kg/m3]
c_drag = 0.3 # drag coefficient
area_b = (4*math.pi*r**2)/2 # surface area of the ball
results = {}
count = 1
tot = len(torq_elb_list) * len(re_angl_deg_list)
for torq_elb in torq_elb_list:
for re_angl_deg in re_angl_deg_list:
results[(torq_elb, re_angl_deg)] = {}
re_angl_rad = math.radians(re_angl_deg )
# Set up variables.
time = np.arange(0, endTime + dt, dt) # A list with all times we want to plot at.
w = np.zeros(len(time)) # A list for the angular velocity. [rad/s]
w_deg = np.zeros(len(time)) # list for angle of angular velocity
tet = np.zeros(len(time)) # A list for the distance.
x_pos = np.zeros(len(time)) # A list for the xpos
y_pos = np.zeros(len(time)) # A list for the ypos.
x_pos_released = np.zeros(len(time)) # A list for the xpos when released
y_pos_released = np.zeros(len(time)) # A list for the ypos when released
v_x = np.zeros(len(time)) # A list for the xpos
v_y = np.zeros(len(time)) # A list for the ypos.
v_t = np.zeros(len(time)) # List for tangent speed
v_ang = np.zeros(len(time)) # list for angle of the tangent speed
air_res = np.zeros(len(time)) # list for total air resistance
air_res_x = np.zeros(len(time)) # list for X vector of air resistance
air_res_y = np.zeros(len(time)) # list for Y vector of air resistance
w[0] = w0 #start w
tet[0] = math.radians(tet0)
x_pos[0] = 0 # xpos start
y_pos[0] = 1.8 # approximate hight of a person that is throwing
released=False
# Run simulation.
for i in range(1, len(time)):
if (released==False):
w[i] = w[i-1] + torq_elb / I *dt
tet[i] = tet[i-1] + w[i] * dt
x_pos[i] = x_pos[i-1] + r * math.cos(w[i] - w[i-1]) * dt
y_pos[i] = y_pos[i-1] + r * math.sin(w[i] - w[i-1]) * dt
if (tet[i] > re_angl_rad) and (released==False):
v_release = w[i] * r
tet_release = tet[i]
v_x[i-1] = v_release * math.cos(tet_release)
v_y[i-1] = v_release * math.sin(tet_release)
x_pos_released[i-1]=x_pos[i]
y_pos_released[i-1]=y_pos[i]
released=True
w[i] = 0
if (released==True):
v_x[i]=v_x[i-1]
v_y[i]=v_y[i-1]
v_t[i] = math.sqrt(v_x[i-1]**2+v_y[i-1]**2)
v_ang[i] = math.atan(v_y[i-1]/v_x[i-1])
air_res[i] = 0.5*rho_air*v_t[i]**2*c_drag*area_b ##Force airresitance
air_res_x[i] = (air_res[i] * math.cos(v_ang[i]))/m_ball
air_res_y[i] = (air_res[i] * math.sin(v_ang[i]))/m_ball
v_x[i]= v_x[i-1] - air_res_x[i] * dt
v_y[i]= v_y[i-1] - (g + air_res_y[i]) * dt
x_pos_released[i] = x_pos_released[i-1] + ((v_x[i-1] + v_x[i])/2) * dt
y_pos_released[i] = y_pos_released[i-1] + ((v_y[i-1] + v_y[i])/2) * dt
# Store simulation results
results[(torq_elb, re_angl_deg)]['time'] = time
results[(torq_elb, re_angl_deg)]['tet'] = tet
results[(torq_elb, re_angl_deg)]['w'] = w
results[(torq_elb, re_angl_deg)]['y_pos_released'] = y_pos_released
results[(torq_elb, re_angl_deg)]['x_pos_released'] = x_pos_released
results[(torq_elb, re_angl_deg)]['v_t'] = v_t
results[(torq_elb, re_angl_deg)]['air_res'] = air_res
print(f'Finished simulation: torque: {torq_elb} release: {re_angl_deg}\t{count} of {tot}')
count+=1
# Display results for a particular (torq, re_angl_deg).
#pip install choice
import choice
print('Choose torque.')
torque_choice = int(choice.Menu([str(x) for x in torq_elb_list.tolist()]).ask())
print('Choose release degree.')
release_choice = int(choice.Menu([str(x) for x in re_angl_deg_list.tolist()]).ask())
time = results[(torque_choice, release_choice)]['time']
tet = results[(torque_choice, release_choice)]['tet']
w = results[(torque_choice, release_choice)]['w']
y_pos_released = results[(torque_choice, release_choice)]['y_pos_released']
x_pos_released = results[(torque_choice, release_choice)]['x_pos_released']
v_t = results[(torque_choice, release_choice)]['v_t']
air_res = results[(torque_choice, release_choice)]['air_res']
plt.plot(time, tet, color='pink',label='Angular Displacement')
plt.plot(time, w, color='yellow', label='Angular Velocity')
plt.plot(time, y_pos_released,color='blue',label='Y_position')
plt.plot(time, x_pos_released,color='purple',label='X_position')
plt.plot(time, v_t, color='black',label='Tangent Velocity')
plt.plot(time, air_res, color='cyan',label='Force Air_res')
plt.xlabel('Time [s]')
plt.ylabel('YYYY')
plt.title('Torque: %s - Release: %s°' %(torque_choice,release_choice))
plt.legend()
plt.xlim(0,1)
plt.ylim(0,10)
plt.show()
plt.plot(x_pos_released,y_pos_released,':',color='green' ,label='Trajectory ball')
plt.xlabel('Distance[m]')
plt.ylabel('Height[m]')
plt.title('Torque: %s - Release: %s°' %(torque_choice,release_choice))
plt.xlim(0,4)
plt.ylim(0,4)
plt.legend()
plt.show()
输入：
Choose torque.
Make a choice:
0: 50
1: 55
2: 60
3: 65
4: 70
5: 75
6: 80
7: 85
8: 90
9: 95
Enter number or name; return for next page
? 0
Choose release degree.
Make a choice:
0: 30
1: 32
2: 34
3: 36
4: 38
5: 40
6: 42
7: 44
8: 45
9: 47
Enter number or name; return for next page
? 4
输出：