def sim(h, N, v_0, x_0):
v = np.zeros(N)
v[0] = v_0
x = np.zeros(N)
x[0] = x_0
t = np.zeros(N)
norm = np.zeros(N)
fric = np.zeros(N)
# Eulers shitty method
for n in range(N - 1):
# Update time and angle for current position
t[n + 1] = t[n] + h
alpha = exlab.slope(lane_h, x[n])
# Store current state for norm and fric
norm[n] = fnorm(v[n], x[n], alpha)
fric[n] = ffric(v[n], x[n], alpha)
# Calculate next states for position and velocity
x[n + 1] = x[n] + h * v[n] * np.cos(alpha)
v[n + 1] = v[n] + 0.5 * h * fv(v[n], alpha)
return t, v, x, norm, fric
def fix_exp_data(exp_data_t, exp_data_v, exp_data_x, FORMAT=False):
# DIfferent parameters if format specified True
if (not FORMAT):
exp_x_offset = -0.05
exp_v_offset = 0.1
else:
exp_x_offset = -0.05
exp_v_offset = 0
# Because v_exp is relative to the horizon and not the track, we need to change this
for n in range(len(exp_data_v)):
alpha = exlab.slope(lane_h, exp_data_x[n])
exp_data_v[n] *= np.cos(alpha)
# Offset data to start at the origin
exp_t_0 = exp_data_t[0]
exp_x_0 = exp_data_x[0]
exp_v_0 = exp_data_v[0]
exp_data_v[0] = 0
for i in range(len(exp_data_t)):
exp_data_t[i] -= exp_t_0
exp_data_x[i] -= exp_x_offset
exp_data_v[i] -= exp_v_0 - exp_v_offset
return exp_data_v, exp_data_x
def test_slope(self):
x = np.array([-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2])
y = x**2
h = height(x, y)
y_interp = h(x)
x_interp = np.linspace(0.2, 0.8, 100)
dydx = 2 * x_interp
angle = -np.arctan(dydx)
s = slope(h, x_interp)
if SHOW:
from matplotlib import pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(x_interp, angle, 'x')
ax.plot(x_interp, s)
plt.show()
self.assertTrue(np.allclose(s, angle, atol=0.01))
def get_time(x, y):
he = height(x, y)
x_interp = np.linspace(0.0, 1.4, 10000)
alpha = slope(he, x_interp)
kappa = curvature(he, x_interp)
N = 10000 # antall steg
h = 0.002 # stegstørrelse
# initialverdier
t_0 = 0
v_0 = 0
x_0 = 0
v_x_0 = 0
no_0 = 0
f_0 = 0
# konstant g/(1+(I_0/mr^2)) for kula
K = 7.007143
m = 0.03
g = 9.81
c = 2 / 5
#kappa = curvature(he_acc, x_interp)
# alpha funksjonen a(x)
a = height(x_interp, alpha)
k = height(x_interp, kappa)
t = np.zeros(N + 1)
v = np.zeros(N + 1)
x = np.zeros(N + 1)
v_x = np.zeros(N + 1)
no = np.zeros(N + 1)
f = np.zeros(N + 1)
t[0] = t_0
v[0] = v_0
x[0] = x_0
v_x[0] = v_x_0
no[0] = no_0
f[0] = f_0
t_old = t_0
v_old = v_0
x_old = x_0
no_old = no_0
f_old = f_0
for n in range(N):
v_new = v_old + h * (K * (np.sin(a(x_old)))) # Euler's method
v_x_new = v_new * np.cos(a(x_old))
x_new = x_old + h * (v_new * np.cos(a(x_old)))
aks = K * (np.sin(a(x_old)))
f_new = m * g * np.sin(a(x_old)) - m * aks
no_new = m * g * np.cos(a(x_old)) + m * v_new**2 / k(x_old)
t[n + 1] = t_old + h
v[n + 1] = v_new
x[n + 1] = x_new
v_x[n + 1] = v_x_new
f[n + 1] = f_new
no[n + 1] = no_new
t_old = t_old + h
v_old = v_new
x_old = x_new
if x_old >= 1.4:
t_ans = t_old - h
N = n
break
t = t[:N]
x = x[:N]
v_x = v_x[:N]
f = f[:N]
no = no[:N]
return x, v, t_ans, t, v_x, f, no
import numpy as np
import matplotlib.pyplot as plt
from eksternlab import height, slope, curvature
from scipy.constants import g
x = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4]
y = [0.472, 0.374, 0.313, 0.280, 0.284, 0.314, 0.373, 0.450]
h = height(x, y)
x_interp = np.linspace(0.0, 1.0, 50)
alpha = slope(h, x_interp)
kappa = curvature(h, x_interp)
plt.plot(h, x_interp)
plt.ylabel('$slope$'), plt.xlabel('$x$')
plt.show()
from pylab import *;plot();show()
x_track = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2]
for i in range(len(x_track)):
x_track[i] *= 0.975
y_track = [0.278, 0.151, 0.08, 0.055, 0.078, 0.151, 0.275] #Høydene vi målte på labben
h = height(x_track, y_track)
print("h:", h)
x_interp = np.linspace(0.0, 1.2,50) #Er lengde fra til med antall intervaller
print("x_interp:", x_interp, len(x_interp))
y_interp = h(x_interp)
print("y_interp:", y_interp, len(y_interp))
alpha = slope(h, x_interp) #Hellingsvinkelen til banen
kappa = curvature(h, x_interp) # Krumningsradiusen til banen.
kappa[0] = kappa[1]
for i in range(len(alpha)):
print("x:", "{:1.3f}".format(x_interp[i]), "y:", "{:1.3f}".format(y_interp[i]), "Alfa:", "{:1.3f}".format(alpha[i]), "Kappa:", "{:1.3f}".format(kappa[i]))
totaltid = 40
iterasjoner = 5000
a = [0]
v = [0.5]
s = [0]
x = [0]
f = [0]
atemp = 0
etemp = 0
rise = True
m = 0.03
r = 0.011
k = 0.4
I = k*m*r*r
gamma = -0.05222142975 #fra eksperiment
c = -1*gamma * 2 * m * (1+k)
numc = 3.75 * (10**(-6)) #teoretisk c
print(f"Snittverdi for c: {c}\n")
g = 9.81
fx = k*m
pps = 1000
h = height(xxlist, hlist)
alpha = (slope(h,xxlist[1]))
avgA=0.3973574765
def accl(alpha, v):
return (g*sin(alpha)-(c*v)/m)/(1 + k)
start = time()
# startverdier for å normalisere listelengde
ntemp = m*vlist[0]*vlist[0]*curvature(h, xlist[0]) + m*g*cos(alpha)
nlist.append(ntemp)
ftemp = fx * accl(alpha, vlist[0])
flist.append(ftemp)
atemp = accl(alpha, vlist[0])
alist.append(atemp)