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Formule de Baza pentru Curbe Plane, Curbe Strambe si Integrala
Simpla
CURBE PLANEReprezentari analitice ale curbelor planeO curba
plana poate fi reprezentata printr-una din urmatoarele ecuatii:
Ecuatia EXPLICITA : y=f(x) Ec. IMPLICITA : f(x,y)=0 Ec.
PARAMETRICE : c(t)=(x(t),y(t)) sau
Ec. VECTORIALA : =x(t)+y(t)
Ec. In COORDONATE POLARE: r=r
ELEMENTUL DE ARC
A. Ec. Parametrica ds=dtB. Ec. Explicita ds=dxC. Ec. In
Coordinate Polare ds=d
LUNGIMEA ARCULUI DE CURBA (AB), unde A(x(a),y(a));
B(x(b),y(b))
A. Ec. Parametrica L(AB)=dtB. Ec. Explicita L(AB)= dxC. Ec. In
Coordinate Polare L(AB)=d
OBSERVATIE: L(AB)=
ECUATIA TANGENTEI intr-un punct M(,) al curbei plane
1) Ec. Implicita (-)
2) Ec. Parametrica
ECUATIA NORMALEI intr-un punct regulat M()
1) Ec. Implicita
2) Ec. Parametrica
SEGMENTELE TANGENTA, NORMALA ,SUBTANGENTA SI SUBNORMALA1. Ec.
Explicita 2. Ec. Parametrica 3. Ec. In Coordinate Polare
MT=|| MT=|| MT=||
MN=|y| MN=|| MN=
ST=|| ST= |y| ST=OT=
SN=|yy| SN=|y| SN=ON=|| CURBURA UNEI CURBE PLANE
1. Ec. Explicita
2. Ec. Parametrica
3. Ec. In Coordinate Polare
RAZA DE CURBURA
R=||PAGE 1
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