def anim(): #Evolucion del pendulo 1 pendulo1.t = pendulo1.t + pendulo1.dt i = pendulo1.t pendulo1.pos = visual.vector( 1, \ -l1*np.cos(theta1_t[i]), l1*np.sin(theta1_t[i]) ) delta_thetha1 = theta1_t[i-1] - theta1_t[i] cuerda1.rotate( 180*delta_thetha1/np.pi, [1.,0.,0] ) #Evolucion del pendulo 2 pendulo2.t = pendulo2.t + pendulo2.dt i = pendulo2.t pendulo2.pos = visual.vector( 2, \ -l2*np.cos(theta2_t[i]), l2*np.sin(theta2_t[i]) ) delta_thetha2 = theta2_t[i-1] - theta2_t[i] cuerda2.rotate( 180*delta_thetha2/np.pi, [1.,0.,0] ) #Evolucion del pendulo 3 pendulo3.t = pendulo3.t + pendulo3.dt i = pendulo3.t pendulo3.pos = visual.vector( 3, \ -l3*np.cos(theta3_t[i]), l3*np.sin(theta3_t[i]) ) delta_thetha3 = theta3_t[i-1] - theta3_t[i] cuerda3.rotate( 180*delta_thetha3/np.pi, [1.,0.,0] ) #Evolucion del pendulo 4 pendulo4.t = pendulo4.t + pendulo4.dt i = pendulo4.t pendulo4.pos = visual.vector( 4, \ -l4*np.cos(theta4_t[i]), l4*np.sin(theta4_t[i]) ) delta_thetha4 = theta4_t[i-1] - theta4_t[i] cuerda4.rotate( 180*delta_thetha4/np.pi, [1.,0.,0] )
def anim(): #Evolucion del pendulo 1 pendulo1.t = pendulo1.t + pendulo1.dt i = pendulo1.t pendulo1.pos = visual.vector( 1, \ -l1*np.cos(theta1_t[i]), l1*np.sin(theta1_t[i]) ) delta_thetha1 = theta1_t[i - 1] - theta1_t[i] cuerda1.rotate(180 * delta_thetha1 / np.pi, [1., 0., 0]) #Evolucion del pendulo 2 pendulo2.t = pendulo2.t + pendulo2.dt i = pendulo2.t pendulo2.pos = visual.vector( 2, \ -l2*np.cos(theta2_t[i]), l2*np.sin(theta2_t[i]) ) delta_thetha2 = theta2_t[i - 1] - theta2_t[i] cuerda2.rotate(180 * delta_thetha2 / np.pi, [1., 0., 0]) #Evolucion del pendulo 3 pendulo3.t = pendulo3.t + pendulo3.dt i = pendulo3.t pendulo3.pos = visual.vector( 3, \ -l3*np.cos(theta3_t[i]), l3*np.sin(theta3_t[i]) ) delta_thetha3 = theta3_t[i - 1] - theta3_t[i] cuerda3.rotate(180 * delta_thetha3 / np.pi, [1., 0., 0]) #Evolucion del pendulo 4 pendulo4.t = pendulo4.t + pendulo4.dt i = pendulo4.t pendulo4.pos = visual.vector( 4, \ -l4*np.cos(theta4_t[i]), l4*np.sin(theta4_t[i]) ) delta_thetha4 = theta4_t[i - 1] - theta4_t[i] cuerda4.rotate(180 * delta_thetha4 / np.pi, [1., 0., 0])
def anim(): #Evolucion de la bola 1 bola1.t = bola1.t + bola1.dt i = bola1.t bola1.pos = visual.vector(x1_t[i], y1_t[i], r1) #Evolucion de la bola 2 bola2.t = bola2.t + bola2.dt i = bola2.t bola2.pos = visual.vector(x2_t[i], y2_t[i], r2) #Evolucion de la bola 3 bola3.t = bola3.t + bola3.dt i = bola3.t bola3.pos = visual.vector(x3_t[i], y3_t[i], r3)
def anim(): #Evolucion de la bola 1 bola1.t = bola1.t + bola1.dt i = bola1.t bola1.pos = visual.vector( x1_t[i], y1_t[i], r1 ) #Evolucion de la bola 2 bola2.t = bola2.t + bola2.dt i = bola2.t bola2.pos = visual.vector( x2_t[i], y2_t[i], r2 ) #Evolucion de la bola 3 bola3.t = bola3.t + bola3.dt i = bola3.t bola3.pos = visual.vector( x3_t[i], y3_t[i], r3 )
def anim(): global theta, phidot, alphadot, M, g, r, thetadot, phi, alpha, t for step in range(Nsteps): # multiple calculation steps for accuracy # Calculate accelerations of the Lagrangian coordinates: atheta = (phidot**2 * sin(theta) * cos(theta) - 2. * (alphadot + phidot * cos(theta)) * phidot * sin(theta) + 2. * M * g * r * sin(theta) / I) aphi = 2. * thetadot * (alphadot - phidot * cos(theta)) / sin(theta) aalpha = phidot * thetadot * sin(theta) - aphi * cos(theta) # Update velocities of the Lagrangian coordinates: thetadot = thetadot + atheta * dt phidot = phidot + aphi * dt alphadot = alphadot + aalpha * dt # Update Lagrangian coordinates: theta = theta + thetadot * dt phi = phi + phidot * dt alpha = alpha + alphadot * dt gyro.axis = vector( sin(theta) * sin(phi), cos(theta), sin(theta) * cos(phi)) # Display approximate rotation of rotor and shaft: gyro.rotate(axis=gyro.axis, angle=alphadot * dt * Nsteps, origin=gyro.pos) trail.append(gyro.pos + gyro.axis * Lshaft) t = t + dt * Nsteps
def anim(): global theta, phidot, alphadot, M, g, r, thetadot, phi, alpha, t for step in range(Nsteps): # multiple calculation steps for accuracy # Calculate accelerations of the Lagrangian coordinates: atheta = (phidot**2*sin(theta)*cos(theta) -2.*(alphadot+phidot*cos(theta))*phidot*sin(theta) +2.*M*g*r*sin(theta)/I) aphi = 2.*thetadot*(alphadot-phidot*cos(theta))/sin(theta) aalpha = phidot*thetadot*sin(theta)-aphi*cos(theta) # Update velocities of the Lagrangian coordinates: thetadot = thetadot+atheta*dt phidot = phidot+aphi*dt alphadot = alphadot+aalpha*dt # Update Lagrangian coordinates: theta = theta+thetadot*dt phi = phi+phidot*dt alpha = alpha+alphadot*dt gyro.axis = vector(sin(theta)*sin(phi),cos(theta),sin(theta)*cos(phi)) # Display approximate rotation of rotor and shaft: gyro.rotate(axis = gyro.axis, angle=alphadot*dt*Nsteps, origin = gyro.pos) trail.append(gyro.pos + gyro.axis * Lshaft) t = t+dt*Nsteps
def main(): # Creating parameters for box size side = 4.0 thk = 0.3 s2 = 2 * side - thk s3 = 2 * side + thk # Creating the 6 walls wallR = box(pos=(side, 0, 0), size=(thk, s3, s2), color=(1, 0, 0)) wallL = box(pos=(-side, 0, 0), size=(thk, s3, s2), color=(1, 0, 0)) wallB = box(pos=(0, -side, 0), size=(s3, thk, s3), color=(0, 0, 1)) wallT = box(pos=(0, side, 0), size=(s3, thk, s3), color=(0, 0, 1)) wallBK = box(pos=(0, 0, -side), size=(s2, s2, thk), color=(0.7, 0.7, 0.7)) # Creating the ball ball = sphere(radius=0.4, color=(0, 1, 0)) ball.vector = vector(-0.15, -0.23, 0.27) side = side - thk * 0.5 - ball.radius ball.t = 0.0 ball.dt = 0.5 def anim(): #Creating the animation function which will be called at #uniform timeperiod through the iterate function ball.t = ball.t + ball.dt ball.pos = ball.pos + ball.vector * ball.dt if not (side > ball.x > -side): ball.vector.x = -ball.vector.x if not (side > ball.y > -side): ball.vector.y = -ball.vector.y if not (side > ball.z > -side): ball.vector.z = -ball.vector.z a = iterate(20, anim) show() return a
def main(): # Creating parameters for box size side = 4.0 thk = 0.3 s2 = 2 * side - thk s3 = 2 * side + thk # Creating the 6 walls wallR = box(pos=(side, 0, 0), size=(thk, s3, s2), color=(1, 0, 0)) wallL = box(pos=(-side, 0, 0), size=(thk, s3, s2), color=(1, 0, 0)) wallB = box(pos=(0, -side, 0), size=(s3, thk, s3), color=(0, 0, 1)) wallT = box(pos=(0, side, 0), size=(s3, thk, s3), color=(0, 0, 1)) wallBK = box(pos=(0, 0, -side), size=(s2, s2, thk), color=(0.7, 0.7, 0.7)) # Creating the ball ball = sphere(radius=0.4, color=(0, 1, 0)) ball.vector = vector(-0.15, -0.23, 0.27) side = side - thk * 0.5 - ball.radius ball.t = 0.0 ball.dt = 0.5 def anim(): # Creating the animation function which will be called at # uniform timeperiod through the iterate function ball.t = ball.t + ball.dt ball.pos = ball.pos + ball.vector * ball.dt if not (side > ball.x > -side): ball.vector.x = -ball.vector.x if not (side > ball.y > -side): ball.vector.y = -ball.vector.y if not (side > ball.z > -side): ball.vector.z = -ball.vector.z a = iterate(20, anim) show() return a
from math import sqrt from enthought.tvtk.tools.visual import sphere, iterate, show, vector, curve #Creating the actors for the scene giant = sphere(pos=(-1.0e11, 0, 0), radius=2e10, color=(1, 0, 0), mass=2e30) dwarf = sphere(pos=(1.5e11, 0, 0), radius=1e10, color=(1, 1, 0), mass=1e30) giant.p = vector(0, 0, -1e4) * giant.mass dwarf.p = -1*giant.p # creating the curve which will trace the paths of actors for a in [giant, dwarf]: a.orbit = curve(radius=2e9, color=a.color) dt = 86400 def anim(): #Creating the animation function which will be called at #uniform timeperiod through the iterate function dist = dwarf.pos - giant.pos force = 6.7e-11 * giant.mass * dwarf.mass * \ dist/(sqrt(dist[0]**2 + dist[1]**2 + dist[2]**2))**3 giant.p = giant.p + force*dt
#!/usr/bin/env python """A simple example demonstrating the creation of actors and animating the in a scene using visual modeule.""" # Author: Raashid Baig <*****@*****.**> # License: BSD Style. from math import sqrt from enthought.tvtk.tools.visual import sphere, iterate, show, vector, curve #Creating the actors for the scene giant = sphere(pos=(-1.0e11, 0, 0), radius=2e10, color=(1, 0, 0), mass=2e30) dwarf = sphere(pos=(1.5e11, 0, 0), radius=1e10, color=(1, 1, 0), mass=1e30) giant.p = vector(0, 0, -1e4) * giant.mass dwarf.p = -1 * giant.p # creating the curve which will trace the paths of actors for a in [giant, dwarf]: a.orbit = curve(radius=2e9, color=a.color) dt = 86400 def anim(): #Creating the animation function which will be called at #uniform timeperiod through the iterate function dist = dwarf.pos - giant.pos force = 6.7e-11 * giant.mass * dwarf.mass * \ dist/(sqrt(dist[0]**2 + dist[1]**2 + dist[2]**2))**3
"Return the magnitude of a vector" return math.sqrt((v*v).sum()) # Geometric parameters (all in MKS units) theta = math.pi/4 # initial angle of gun D = 20 # width ... H = 20 # height of floor g = -9.8 # gravity gun_len = 2 # size of gun arrow_len = 4 # and of arrow v0_default = 15 # default for initial velocity if not given # Numerical simulation parameters dt = 0.01 # Update for all velocities under constant acceleration (gravity) dv = V.vector(0,g*dt,0) # Tolerance for deciding whether a collision happened impact_distance = 0.5 # Initialize arguments try: v0 = float(sys.argv[1]) except: v0 = v0_default print 'Using default v0 =',v0,'m/s.' # Build 3d world # Define the line of sight sight = V.vector(math.cos(theta),math.sin(theta),0)
from enthought.tvtk.tools.visual import curve, box, vector, show from numpy import arange, array lorenz = curve( color = (1,1,1), radius=0.3 ) # Draw grid for x in xrange(0,51,10): curve(points = [[x,0,-25],[x,0,25]], color = (0,0.5,0), radius = 0.3 ) box(pos=(x,0,0), axis=(0,0,50), height=0.4, width=0.4, length = 50) for z in xrange(-25,26,10): curve(points = [[0,0,z], [50,0,z]] , color = (0,0.5,0), radius = 0.3 ) box(pos=(25,0,z), axis=(50,0,0), height=0.4, width=0.4, length = 50) dt = 0.01 y = vector(35.0, -10.0, -7.0) pts = [] for i in xrange(2000): # Integrate a funny differential equation dydt = vector( -8.0/3*y[0] + y[1]*y[2], - 10*y[1] + 10*y[2], - y[1]*y[0] + 28*y[1] - y[2]) y = y + dydt * dt pts.append(y) if len(pts) > 20: lorenz.extend(pts) pts[:] = [] show()
# The Lagrangian variables are polar angle theta, # azimuthal angle phi, and spin angle alpha. Lshaft = 1. # length of gyroscope shaft Rshaft = 0.03 # radius of gyroscope shaft M = 1. # mass of gyroscope (massless shaft) Rrotor = 0.4 # radius of gyroscope rotor Drotor = 0.1 # thickness of gyroscope rotor Dsquare = 1.4*Drotor # thickness of square that turns with rotor I = 0.5*M*Rrotor**2. # moment of inertia of gyroscope hpedestal = Lshaft # height of pedestal wpedestal = 0.1 # width of pedestal tbase = 0.05 # thickness of base wbase = 3.*wpedestal # width of base g = 9.8 Fgrav = vector(0,-M*g,0) top = vector(0,0,0) # top of pedestal theta = pi/3. # initial polar angle of shaft (from vertical) thetadot = 0 # initial rate of change of polar angle alpha = 0 # initial spin angle alphadot = 15 # initial rate of change of spin angle (spin ang. velocity) phi = -pi/2. # initial azimuthal angle phidot = 0 # initial rate of change of azimuthal angle # Comment in following line to get pure precession ##phidot = (-alphadot+sqrt(alphadot**2+2*M*g*r*cos(theta)/I))/cos(theta) pedestal = box(pos=top-vector(0,hpedestal/2.,0), height=hpedestal, length=wpedestal, width=wpedestal, color=(0.4,0.4,0.5)) base = box(pos=top-vector(0,hpedestal+tbase/2.,0),
#!/usr/bin/env python # Author: Raashid Baig <*****@*****.**> # License: BSD Style. # Gyroscope hanging from a spring from math import atan, cos, sin, pi from enthought.tvtk.tools.visual import vector, MVector, Box, Helix, Frame, \ Cylinder, curve, color, iterate, show top = vector(0,1.,0) # where top of spring is held ks = 100. # spring stiffness Lspring = 1. # unstretched length of spring Rspring = 0.03 # radius of spring Dspring = 0.03 # thickness of spring wire Lshaft = 1. # length of gyroscope shaft Rshaft = 0.03 # radius of gyroscope shaft M = 1. # mass of gyroscope (massless shaft) Rrotor = 0.4 # radius of gyroscope rotor Drotor = 0.1 # thickness of gyroscope rotor Dsquare = 1.4*Drotor # thickness of square that turns with rotor I = 0.5*M*Rrotor**2. # moment of inertia of gyroscope omega = 40.0 # angular velocity of rotor along axis g = 9.8 Fgrav = MVector(0,-M*g,0) precession = M*g*(Lshaft/2.)/(I*abs(omega)) # exact precession angular velocity phi = atan(precession**2*(Lshaft/2.)/g) # approximate angle of spring to vertical s = M*g/(ks*cos(phi)) # approximate stretch of spring # Refine estimate of angle of spring to vertical:
#!/usr/bin/env python # Author: Raashid Baig <*****@*****.**> # License: BSD Style. # Gyroscope hanging from a spring from math import atan, cos, sin, pi from enthought.tvtk.tools.visual import vector, MVector, Box, Helix, Frame, \ Cylinder, curve, color, iterate, show top = vector(0, 1., 0) # where top of spring is held ks = 100. # spring stiffness Lspring = 1. # unstretched length of spring Rspring = 0.03 # radius of spring Dspring = 0.03 # thickness of spring wire Lshaft = 1. # length of gyroscope shaft Rshaft = 0.03 # radius of gyroscope shaft M = 1. # mass of gyroscope (massless shaft) Rrotor = 0.4 # radius of gyroscope rotor Drotor = 0.1 # thickness of gyroscope rotor Dsquare = 1.4 * Drotor # thickness of square that turns with rotor I = 0.5 * M * Rrotor**2. # moment of inertia of gyroscope omega = 40.0 # angular velocity of rotor along axis g = 9.8 Fgrav = MVector(0, -M * g, 0) precession = M * g * (Lshaft / 2.) / (I * abs(omega) ) # exact precession angular velocity phi = atan(precession**2 * (Lshaft / 2.) / g) # approximate angle of spring to vertical s = M * g / (ks * cos(phi)) # approximate stretch of spring
from enthought.tvtk.tools.visual import curve, box, vector, show from numpy import arange, array lorenz = curve(color=(1, 1, 1), radius=0.3) # Draw grid for x in xrange(0, 51, 10): curve(points=[[x, 0, -25], [x, 0, 25]], color=(0, 0.5, 0), radius=0.3) box(pos=(x, 0, 0), axis=(0, 0, 50), height=0.4, width=0.4, length=50) for z in xrange(-25, 26, 10): curve(points=[[0, 0, z], [50, 0, z]], color=(0, 0.5, 0), radius=0.3) box(pos=(25, 0, z), axis=(50, 0, 0), height=0.4, width=0.4, length=50) dt = 0.01 y = vector(35.0, -10.0, -7.0) pts = [] for i in xrange(2000): # Integrate a funny differential equation dydt = vector(-8.0 / 3 * y[0] + y[1] * y[2], -10 * y[1] + 10 * y[2], -y[1] * y[0] + 28 * y[1] - y[2]) y = y + dydt * dt pts.append(y) if len(pts) > 20: lorenz.extend(pts) pts[:] = [] show()
# The Lagrangian variables are polar angle theta, # azimuthal angle phi, and spin angle alpha. Lshaft = 1. # length of gyroscope shaft Rshaft = 0.03 # radius of gyroscope shaft M = 1. # mass of gyroscope (massless shaft) Rrotor = 0.4 # radius of gyroscope rotor Drotor = 0.1 # thickness of gyroscope rotor Dsquare = 1.4 * Drotor # thickness of square that turns with rotor I = 0.5 * M * Rrotor**2. # moment of inertia of gyroscope hpedestal = Lshaft # height of pedestal wpedestal = 0.1 # width of pedestal tbase = 0.05 # thickness of base wbase = 3. * wpedestal # width of base g = 9.8 Fgrav = vector(0, -M * g, 0) top = vector(0, 0, 0) # top of pedestal theta = pi / 3. # initial polar angle of shaft (from vertical) thetadot = 0 # initial rate of change of polar angle alpha = 0 # initial spin angle alphadot = 15 # initial rate of change of spin angle (spin ang. velocity) phi = -pi / 2. # initial azimuthal angle phidot = 0 # initial rate of change of azimuthal angle # Comment in following line to get pure precession ##phidot = (-alphadot+sqrt(alphadot**2+2*M*g*r*cos(theta)/I))/cos(theta) pedestal = box(pos=top - vector(0, hpedestal / 2., 0), height=hpedestal, length=wpedestal, width=wpedestal,
L2 = 1.0 # physical length of lower bar L2display = L2+d/2. # show lower bar a bit longer than physical, to overlap axle # Coefficients used in Lagrangian calculation A = (1./4.)*M1*L1**2+(1./12.)*M1*L1**2+M2*L1**2 B = (1./2.)*M2*L1*L2 C = g*L1*(M1/2.+M2) D = M2*L1*L2/2. E = (1./12.)*M2*L2**2+(1./4.)*M2*L2**2 F = g*L2*M2/2. hpedestal = 1.3*(L1+L2) # height of pedestal wpedestal = 0.1 # width of pedestal tbase = 0.05 # thickness of base wbase = 8.*gap # width of base offset = 2.*gap # from center of pedestal to center of U-shaped upper assembly top = vector(0,0,0) # top of inner bar of U-shaped upper assembly theta1 = 1.3*pi/2. # initial upper angle (from vertical) theta1dot = 0 # initial rate of change of theta1 theta2 = 0 # initial lower angle (from vertical) theta2dot = 0 # initial rate of change of theta2 pedestal = box(pos = (top - vector(0, hpedestal/2.0, offset)),size = (wpedestal, 1.1*hpedestal, wpedestal), color = (0.4,0.4,0.5)) base = box(pos = (top - vector(0,hpedestal + tbase/2.0, offset)),size=(wbase, tbase, wbase),color = (0.4,0.4,0.5)) bar1 = box(pos=(L1display/2.0 - d/2.0, 0, -(gap+d)/2.0), size=(L1display, d, d), color=(1,0,0)) bar1b = box(pos=(L1display/2.0 - d/2.0, 0, (gap+d)/2.0), size=(L1display, d, d), color=(1,0,0)) frame1 = frame(bar1, bar1b) frame1.pos = (0.0, 0.0, 0.0)