Examen d'août 2013: réponses numériques

---- Q1 ----
Intersection for φ₁: (0.5, 0.866025) (déterminable à la main!)
Intersection for φ₂: (0.963525, -0.267617)
---- Q2 ----
u₀ = 0, u₁ = 0.10472, u₅ = 0.500895, u_30 = -0.00143922
e(-u, 30) = 0.00148411
p ≈ 2.002170
---- Q3 ----
c = -5 => speed at jump: (3.13209, 6.26418), norm: 7.00357;  d = 4
c = -6 => speed at jump: (4.85222, 9.70443), norm: 10.8499;  d = 9.6
μ₁=0    c= -5 => at jump: t=1.46752, v=(3.13208, 6.26415), |v|=7.00353;  d = 3.99996
μ₁=0    c= -6 => at jump: t=1.65701, v=(4.85222, 9.70444), |v|=10.8499;  d = 9.60002
μ₁=0.25 c= -5 => at jump: t=1.61188, v=(2.06433, 4.12866), |v|=4.61598;  d = 1.7376
μ₁=0.25 c= -6 => at jump: t=1.80134, v=(3.6392, 7.2784), |v|=8.1375;  d = 5.40012
μ₁=0.5  c=-10 => at jump: t=3.58284, v=(5.41058, 10.8212), |v|=12.0984;  d = 11.9365
See "exam130816-S.pdf" for the graphs of S(t)
μ₁ = 0.25, μ₂ = 0.1, c = -5 => time to reach P₁ = 3.08128
μ₁ = 0.25, μ₂ = 0.1, c = -6 => time to reach P₁ = 3.7345
P₂ = (d,0) + η(6.15958) = (d + 6.15958, 1.23293)
μ₁ = 0.25, μ₂ = 1.7 => c = -4.74705
Modifié le: samedi 17 août 2013, 14:19