- #1
eljose
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Let be a differential equation :
y^{(n)}=F(t,y,\dot y ,\ddot y , \dddot y,..., y^{n-1})
then if we propose a Lagrangian so its euler-Lagrange equation gives:
\sum_{k=0}^{n}(-1)^{n}\frac{d^{2}}{dt^{2}}(\frac{\partial ^{n} L}{\partial \ y^{n} })=0
The differential equation can be derived from a variational principle...then my question is how could we applycontinous group theory to solve this differential equation thanks,or for example if i know that the differential equation has as a particular solution y(t)=exp(rt) where r can be a real or complex parameter.
y^{(n)}=F(t,y,\dot y ,\ddot y , \dddot y,..., y^{n-1})
then if we propose a Lagrangian so its euler-Lagrange equation gives:
\sum_{k=0}^{n}(-1)^{n}\frac{d^{2}}{dt^{2}}(\frac{\partial ^{n} L}{\partial \ y^{n} })=0
The differential equation can be derived from a variational principle...then my question is how could we applycontinous group theory to solve this differential equation thanks,or for example if i know that the differential equation has as a particular solution y(t)=exp(rt) where r can be a real or complex parameter.
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