%pylab inline
import matplotlib.pyplot as plt

from scipy.optimize import fsolve

from ipywidgets import *

Populating the interactive namespace from numpy and matplotlib

Relativisztikus biciklikerék

Hogyan látjuk a közel fénysebességgel haladó biciklikerék küllőit?

Lásd még:

phys.org/news (August 10, 2012) RIKEN

What does an object look like when moving at nearly the speed of light?

Phys. Rev Letters, 2012

R. A. Muller, Am. J. Phys. 60, 313 (1992)

Visualisation in special and general relativity

Daniel Weiskopf: Visualization of Four-Dimensional Spacetimes, Thesis

def func(t,param1):
    V, om, r, fi = param1 # r in units of R, om in units of om=omega*R/c
    
    tmp= t-V*r*sin(om*t+fi)
    return(tmp)
    

def trafo(t,param):
    V, om, r, fi = param # r in units of R, om in units of om=omega*R/c
    gamma=1/sqrt(1-V**2)
    xv=gamma*(-V+r*sin(om*t+fi))
    zv=r*cos(om*t+fi)
    return([xv,zv])

def flywheel(r,fi,param):
    V, om = param # r in units of R, om in units of om=omega*R/c
    param1 = [param[0],param[1],r, fi]

    tsol=fsolve(func,0,param1)
    
    #  Lorentz-trafo
    gamma=1/sqrt(1-V**2)
    xv=gamma*(-V*tsol+r*sin(om*tsol[0]+fi))
    zv=r*cos(om*tsol[0]+fi)
    return([xv,zv])
    

#param=[V,om,r, fi]
param=[0.7,0.7]
param1=[param[0],param[1],0.27,pi/6]

func(0,param1)

-0.09449999999999999

A bicikli sebessége: $V= 0.7c$, és $\omega R = 0.7 c$

rvec=linspace(0,1,100)
#param=[V,om]
param=[0.7,0.7]

close('all')
#figure(figsize=(12, 12))

# Two subplots, unpack the axes array immediately
fig, (ax1, ax2) = subplots(1, 2,figsize=(16, 8),sharex=True)

ax1.set_title('A bicikli rendszerében',fontsize=16)
ax2.set_title('Laboratóriumi rendszerben',fontsize=16)
ax1.set_aspect('equal')
ax2.set_aspect('equal')

fivec=linspace(0,2*pi,18)

tt=linspace(0,2*pi,100)
ax1.plot(cos(tt),sin(tt),color='k')

for fi in fivec:
    ax1.plot([0,cos(fi)],[0,sin(fi)],color='k')

for fi in fivec:
    xx=[]
    zz=[]
    for rr in rvec:
        
        xz=flywheel(rr,fi,param)

        xx.append(xz[0])
        zz.append(xz[1])
    
    ax2.plot(xx,zz,color='blue')

fivec=linspace(0,2*pi,100)
xxlast=[]  
zzlast=[]
for fi in fivec:
    xzlast=flywheel(1,fi,param)
    xxlast.append(xzlast[0])
    zzlast.append(xzlast[1])

ax2.plot(xxlast,zzlast,color='red')

#tight_layout()

ax1.grid();
ax2.grid();