In [1]:
import sympy as sp
sp.init_printing()
In [2]:
R, r, r1, eps1, m, ths, mu0, mu, g = sp.symbols("R r r1 eps1 m ths mu0 mu g")
adat=[(R, 450e-3), (r, 150e-3), (r1, 250e-3), (eps1, 3), (m, 70), (ths, 4.375), (mu0, 0.25), (mu, 0.2), (g, 9.81)]
In [3]:
aSx, K, Cx, Cy, eps2 = sp.symbols("aSx K Cx Cy eps2")
# 0-ra rendezve
dinalaptetelx = - m * aSx - (-K + Cx)
dinalaptetely = - m * 0 - (-m*g + Cy)
dinalaptetelz = ths*eps2 - (-K * r + Cx * R)
# Tegyük fel, hogy gördül
kin1 = aSx - R*eps2
aDx, aEx = sp.symbols("aDx aEx")
kin2 = aDx - (-(R-r)*eps2)
kin3 = aEx - (-r1*eps1)
kin4 = aDx - aEx
In [4]:
mego = sp.solve([dinalaptetelx, dinalaptetely, dinalaptetelz, kin1, kin2, kin3, kin4], [K, Cx, Cy, eps2, aSx, aDx, aEx])
mego
Out[4]:
$$\left \{ Cx : \frac{eps_{1} r_{1} \left(R m r + ths\right)}{R^{2} - 2 R r + r^{2}}, \quad Cy : g m, \quad K : \frac{eps_{1} r_{1} \left(R^{2} m + ths\right)}{R^{2} - 2 R r + r^{2}}, \quad aDx : - eps_{1} r_{1}, \quad aEx : - eps_{1} r_{1}, \quad aSx : \frac{R eps_{1} r_{1}}{R - r}, \quad eps_{2} : \frac{eps_{1} r_{1}}{R - r}\right \}$$
In [5]:
Cx.subs(mego).subs(adat)
Out[5]:
$$75.8333333333333$$
In [6]:
Cy.subs(mego).subs(adat)
Out[6]:
$$686.7$$
In [7]:
K.subs(mego).subs(adat)
Out[7]:
$$154.583333333333$$
In [8]:
aSx.subs(mego).subs(adat)
Out[8]:
$$1.125$$
In [9]:
eps2.subs(mego).subs(adat)
Out[9]:
$$2.5$$
In [10]:
(Cx/Cy).subs(mego).subs(adat)
Out[10]:
$$0.110431532449881$$