cours 5
1.5 COURBURE
Au dernier cours, nous avons vu
Au dernier cours, nous avons vu
Intégrale d’une fonction vectorielle
Au dernier cours, nous avons vu
Intégrale d’une fonction vectorielle La longueur d’une courbe
Au dernier cours, nous avons vu
Intégrale d’une fonction vectorielle La longueur d’une courbe
L’abscisse curviligne
Au dernier cours, nous avons vu
Intégrale d’une fonction vectorielle La longueur d’une courbe
L’abscisse curviligne Repère de Frenet
Aujourd’hui, nous allons voir
Aujourd’hui, nous allons voir
Courbure
Aujourd’hui, nous allons voir
Courbure
Le plan et le cercle osculateur
Aujourd’hui, nous allons voir
Courbure
Le plan et le cercle osculateur Formule pour la courbure
Lors de notre exploration du repère de Frenet, on a vu
Lors de notre exploration du repère de Frenet, on a vu
T~ (t) = ~r 0(t) k~r 0(t)k
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Lors de notre exploration du repère de Frenet, on a vu
T~ (t) = ~r 0(t) k~r 0(t)k
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N~ (t) = T~0(t) kT~0(t)k
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Lors de notre exploration du repère de Frenet, on a vu
T~ (t) = ~r 0(t) k~r 0(t)k
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N~ (t) = T~0(t) kT~0(t)k
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B~ (t) = T~(t) ^ N~ (t)
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Lors de notre exploration du repère de Frenet, on a vu
T~ (t) = ~r 0(t) k~r 0(t)k
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N~ (t) = T~0(t) kT~0(t)k
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B~ (t) = T~(t) ^ N~ (t)
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On peut réécrire ces équations en terme de l’abscisse curviligne
T~ (s) = d
ds~r(s)
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T~ (s) = d
ds~r(s)
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N~ (s) =
d
ds T~(s)
d
ds T~(s)
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T~ (s) = d
ds~r(s)
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N~ (s) =
d
ds T~(s)
d
ds T~(s)
<latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit><latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit><latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit><latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit>
B~ (s) = T~(s) ^ N~ (s)
<latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit><latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit><latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit><latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit>
Regardons de plus près
d
ds T~(s) = d
ds T~ (s) N~ (s)
<latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit><latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit><latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit><latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit>
T~ (s) = d
ds~r(s)
<latexit sha1_base64="0/jE7PAZj0zOwHrGfDP2bt+rays=">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</latexit><latexit sha1_base64="0/jE7PAZj0zOwHrGfDP2bt+rays=">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</latexit><latexit sha1_base64="0/jE7PAZj0zOwHrGfDP2bt+rays=">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</latexit><latexit sha1_base64="0/jE7PAZj0zOwHrGfDP2bt+rays=">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</latexit>
N~ (s) =
d
ds T~(s)
d
ds T~(s)
<latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">AAADE3icjVFBT9RAGH1UEETRRY9eGjYmeCFdQqIXE4IXTwQTFkgoIe3s7DKh2zYzUxJS+jP8J968Ga6cjV7lAP+CN0NJFCQ4Tadv3vve63wzaZkpY6Po50TwaHLq8fTMk9mnz+aev+jMv9wyRaWF7IsiK/ROmhiZqVz2rbKZ3Cm1TMZpJrfTw49O3z6S2qgi37THpdwbJ6NcDZVILKn9znp8JEW4vmjefoiHOhH19TwIm3pgGi9uUmzqOJNDG5/8W461Gh1QbfY73Wgp8iO8C3ot6KIdG0XnB2IMUECgwhgSOSxxhgSGzy56iFCS20NNThMpr0s0mKW3YpVkRUL2kPOIq92Wzbl2mca7Bf+S8dV0hnhDT8E6Tez+Fnq98smOvS+79plub8f8pm3WmKzFAdmHfDeV/+tzvVgM8d73oNhT6RnXnWhTKn8qbufhH11ZJpTkHB5Q18TCO2/OOfQe43t3Z5t4/cJXOtatRVtb4dLtkhfcu32dd8HW8lKP+PNKd3WtveoZvMYCFnmf77CKT9hAn9lf8Qu/cR58Cb4F34PT69JgovW8wl8jOLsCRS6vhA==</latexit><latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit><latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit><latexit sha1_base64="sfQnGme65S3aZZBWRSO4AGgaXD8=">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</latexit>
B~ (s) = T~(s) ^ N~ (s)
<latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit><latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit><latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit><latexit sha1_base64="9C1Nd+n+hCOjoJZJeJCSuso+gfA=">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</latexit>
d
ds T~ (s) = d
ds T~(s) N~ (s)
<latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit><latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit><latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit><latexit sha1_base64="Cu9p3LNFyhBhrqFasnzwPX5B0Ug=">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</latexit>
C<latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit> 1
d
ds T~ (s) = d
ds T~(s) N~ (s)
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C<latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit> 1 C<latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">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</latexit><latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">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</latexit><latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">AAACz3icjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFnsxmUL9gFtKZPptA3Ni2SilKK49Qfc6l+Jf6B/4Z0xBbWITkhy5tx7zsy914k8N5GW9ZozlpZXVtfy64WNza3tneLuXjMJ05iLBg+9MG47LBGeG4iGdKUn2lEsmO94ouVMqireuhZx4obBlZxGouezUeAOXc4kUd2uz+SYM8+s9k/6xZJVtvQyF4GdgRKyVQuLL+higBAcKXwIBJCEPTAk9HRgw0JEXA8z4mJCro4L3KJA2pSyBGUwYif0HdGuk7EB7ZVnotWcTvHojUlp4og0IeXFhNVppo6n2lmxv3nPtKe625T+TublEysxJvYv3TzzvzpVi8QQ57oGl2qKNKOq45lLqruibm5+qUqSQ0ScwgOKx4S5Vs77bGpNomtXvWU6/qYzFav2PMtN8a5uSQO2f45zETRPyjbh+mmpcpGNOo8DHOKY5nmGCi5RQ4O8IzziCc9G3bgx7oz7z1Qjl2n28W0ZDx/rZZOd</latexit><latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">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</latexit> 2
d
ds T~ (s) = d
ds T~(s) N~ (s)
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C<latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit><latexit sha1_base64="LdVHkxELOuJRz/5C1e4Dk/MIAVk=">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</latexit> 1 C<latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">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</latexit><latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">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</latexit><latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">AAACz3icjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFnsxmUL9gFtKZPptA3Ni2SilKK49Qfc6l+Jf6B/4Z0xBbWITkhy5tx7zsy914k8N5GW9ZozlpZXVtfy64WNza3tneLuXjMJ05iLBg+9MG47LBGeG4iGdKUn2lEsmO94ouVMqireuhZx4obBlZxGouezUeAOXc4kUd2uz+SYM8+s9k/6xZJVtvQyF4GdgRKyVQuLL+higBAcKXwIBJCEPTAk9HRgw0JEXA8z4mJCro4L3KJA2pSyBGUwYif0HdGuk7EB7ZVnotWcTvHojUlp4og0IeXFhNVppo6n2lmxv3nPtKe625T+TublEysxJvYv3TzzvzpVi8QQ57oGl2qKNKOq45lLqruibm5+qUqSQ0ScwgOKx4S5Vs77bGpNomtXvWU6/qYzFav2PMtN8a5uSQO2f45zETRPyjbh+mmpcpGNOo8DHOKY5nmGCi5RQ4O8IzziCc9G3bgx7oz7z1Qjl2n28W0ZDx/rZZOd</latexit><latexit sha1_base64="VspkTx0pCb8o3hhE9YTNj9+qj+g=">AAACz3icjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFnsxmUL9gFtKZPptA3Ni2SilKK49Qfc6l+Jf6B/4Z0xBbWITkhy5tx7zsy914k8N5GW9ZozlpZXVtfy64WNza3tneLuXjMJ05iLBg+9MG47LBGeG4iGdKUn2lEsmO94ouVMqireuhZx4obBlZxGouezUeAOXc4kUd2uz+SYM8+s9k/6xZJVtvQyF4GdgRKyVQuLL+higBAcKXwIBJCEPTAk9HRgw0JEXA8z4mJCro4L3KJA2pSyBGUwYif0HdGuk7EB7ZVnotWcTvHojUlp4og0IeXFhNVppo6n2lmxv3nPtKe625T+TublEysxJvYv3TzzvzpVi8QQ57oGl2qKNKOq45lLqruibm5+qUqSQ0ScwgOKx4S5Vs77bGpNomtXvWU6/qYzFav2PMtN8a5uSQO2f45zETRPyjbh+mmpcpGNOo8DHOKY5nmGCi5RQ4O8IzziCc9G3bgx7oz7z1Qjl2n28W0ZDx/rZZOd</latexit> 2
T~ 0(a) = lim
h!0
T~ (a + h) T~(a) h
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d
ds T~ (s) = d
ds T~(s) N~ (s)
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