This is for a solid sphere of radius R rolling down a hemisphere of radius 5R. please help me understand how to produce these 3 equations. Thank you! the holonomic constraint equations are g₁ (r, 0,6)=r-6R = 0 and I 92 (r,0,0) = Ro-5R0 = 0 1 L (r,0,0) = mr² + mr²0² +mR²² - mgrcos (0) produce three Euler-Lagrange equations. SL & (st) - 5 dt d dt SL (54) SL dø dgi = √₁ 501 + X₂ 50 = ₁80 Σ do δ SL = ₁ + x₂ = ₁5 - - Σ 80 d (#²) - => ₁ &U λ * dgi + √₂/7 = [₁ 50/4 λ Σ dr
This is for a solid sphere of radius R rolling down a hemisphere of radius 5R. please help me understand how to produce these 3 equations. Thank you! the holonomic constraint equations are g₁ (r, 0,6)=r-6R = 0 and I 92 (r,0,0) = Ro-5R0 = 0 1 L (r,0,0) = mr² + mr²0² +mR²² - mgrcos (0) produce three Euler-Lagrange equations. SL & (st) - 5 dt d dt SL (54) SL dø dgi = √₁ 501 + X₂ 50 = ₁80 Σ do δ SL = ₁ + x₂ = ₁5 - - Σ 80 d (#²) - => ₁ &U λ * dgi + √₂/7 = [₁ 50/4 λ Σ dr
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Transcribed Image Text:This is for a solid sphere of radius R rolling down a hemisphere of radius 5R.
please help me understand how to produce these 3 equations. Thank you!
the holonomic constraint equations are g₁ (r, 0, 0) = r — 6R = 0 and
92 (r, 0, 0) = Ro-5R0=0
L (r, 0, 0) =
{
mr² + 1/{mr²0² + / mR²² - mgrcos (0)
produce three Euler-Lagrange equations.
SL
d (4) - 500
dt
SL
(S)
d
dt
d ($)
dt
-
-
8g2
+1₂50/200 dgi
Σi
dø
δὲ
№₁0% + A2
1
δL = λ + λ = Σ
SL
80
80
sgt
80
8gi
SL
61 = A₁ / + √₂/² = Σ₁ %fh
λ
dr
dr
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