Ejemplo n.º 1
0
def _rectForce(x,pot,t=0.):
    """
    NAME:
       _rectForce
    PURPOSE:
       returns the force in the rectangular frame
    INPUT:
       x - current position
       t - current time
       pot - (list of) Potential instance(s)
    OUTPUT:
       force
    HISTORY:
       2011-02-02 - Written - Bovy (NYU)
    """
    #x is rectangular so calculate R and phi
    R= nu.sqrt(x[0]**2.+x[1]**2.)
    phi= nu.arccos(x[0]/R)
    sinphi= x[1]/R
    cosphi= x[0]/R
    if x[1] < 0.: phi= 2.*nu.pi-phi
    #calculate forces
    Rforce= evaluateplanarRforces(R,pot,phi=phi,t=t)
    phiforce= evaluateplanarphiforces(R,pot,phi=phi,t=t)
    return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
                     sinphi*Rforce+1./R*cosphi*phiforce])
Ejemplo n.º 2
0
def _external_force(x,t,pot):
    dim= len(x)
    if dim == 3:
        #x is rectangular so calculate R and phi
        R= nu.sqrt(x[0]**2.+x[1]**2.)
        phi= nu.arccos(x[0]/R)
        sinphi= x[1]/R
        cosphi= x[0]/R
        if x[1] < 0.: phi= 2.*nu.pi-phi
        #calculate forces
        Rforce= evaluateRforces(R,x[2],pot,phi=phi,t=t)
        phiforce= evaluatephiforces(R,x[2],pot,phi=phi,t=t)
        return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
                     sinphi*Rforce+1./R*cosphi*phiforce,
                     evaluatezforces(R,x[2],pot,phi=phi,t=t)])
    elif dim == 2:
        #x is rectangular so calculate R and phi
        R= nu.sqrt(x[0]**2.+x[1]**2.)
        phi= nu.arccos(x[0]/R)
        sinphi= x[1]/R
        cosphi= x[0]/R
        if x[1] < 0.: phi= 2.*nu.pi-phi
        #calculate forces
        Rforce= evaluateplanarRforces(R,pot,phi=phi,t=t)
        phiforce= evaluateplanarphiforces(R,pot,phi=phi,t=t)
        return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
                         sinphi*Rforce+1./R*cosphi*phiforce])
    elif dim == 1:
        return evaluatelinearForces(x,pot,t=t)
Ejemplo n.º 3
0
def _EOM_dxdv(x,t,pot):
    """
    NAME:
       _EOM_dxdv
    PURPOSE:
       implements the EOM, i.e., the right-hand side of the differential 
       equation, for integrating phase space differences, rectangular
    INPUT:
       x - current phase-space position
       t - current time
       pot - (list of) Potential instance(s)
    OUTPUT:
       dy/dt
    HISTORY:
       2011-10-18 - Written - Bovy (NYU)
    """
    #x is rectangular so calculate R and phi
    R= nu.sqrt(x[0]**2.+x[1]**2.)
    phi= nu.arccos(x[0]/R)
    sinphi= x[1]/R
    cosphi= x[0]/R
    if x[1] < 0.: phi= 2.*nu.pi-phi
    #calculate forces
    Rforce= evaluateplanarRforces(R,pot,phi=phi,t=t)
    phiforce= evaluateplanarphiforces(R,pot,phi=phi,t=t)
    R2deriv= evaluateplanarPotentials(R,pot,phi=phi,t=t,dR=2)
    phi2deriv= evaluateplanarPotentials(R,pot,phi=phi,t=t,dphi=2)
    Rphideriv= evaluateplanarPotentials(R,pot,phi=phi,t=t,dR=1,dphi=1)
    #Calculate derivatives and derivatives+time derivatives
    dFxdx= -cosphi**2.*R2deriv\
           +2.*cosphi*sinphi/R**2.*phiforce\
           +sinphi**2./R*Rforce\
           +2.*sinphi*cosphi/R*Rphideriv\
           -sinphi**2./R**2.*phi2deriv
    dFxdy= -sinphi*cosphi*R2deriv\
           +(sinphi**2.-cosphi**2.)/R**2.*phiforce\
           -cosphi*sinphi/R*Rforce\
           -(cosphi**2.-sinphi**2.)/R*Rphideriv\
           +cosphi*sinphi/R**2.*phi2deriv
    dFydx= -cosphi*sinphi*R2deriv\
           +(sinphi**2.-cosphi**2.)/R**2.*phiforce\
           +(sinphi**2.-cosphi**2.)/R*Rphideriv\
           -sinphi*cosphi/R*Rforce\
           +sinphi*cosphi/R**2.*phi2deriv
    dFydy= -sinphi**2.*R2deriv\
           -2.*sinphi*cosphi/R**2.*phiforce\
           -2.*sinphi*cosphi/R*Rphideriv\
           +cosphi**2./R*Rforce\
           -cosphi**2./R**2.*phi2deriv
    return nu.array([x[2],x[3],
                     cosphi*Rforce-1./R*sinphi*phiforce,
                     sinphi*Rforce+1./R*cosphi*phiforce,
                     x[6],x[7],
                     dFxdx*x[4]+dFxdy*x[5],
                     dFydx*x[4]+dFydy*x[5]])
Ejemplo n.º 4
0
def _EOM(y,t,pot):
    """
    NAME:
       _EOM
    PURPOSE:
       implements the EOM, i.e., the right-hand side of the differential 
       equation
    INPUT:
       y - current phase-space position
       t - current time
       pot - (list of) Potential instance(s)
       l2 - angular momentum squared
    OUTPUT:
       dy/dt
    HISTORY:
       2010-07-20 - Written - Bovy (NYU)
    """
    l2= (y[0]**2.*y[3])**2.
    return [y[1],
            l2/y[0]**3.+evaluateplanarRforces(y[0],pot,phi=y[2],t=t),
            y[3],
            1./y[0]**2.*(evaluateplanarphiforces(y[0],pot,phi=y[2],t=t)-
                         2.*y[0]*y[1]*y[3])]