Jacobi integral

to get instant updates about 'Jacobi Integral' on your MyPage. Meet other similar minded people. Its Free!

X 

All Updates


Description:
In celestial mechanics, Jacobi's integral (named after Carl Gustav Jacob Jacobi) is the only known conserved quantity for the restricted three-body problem problem ; unlike in the two-body problem, the energy and momentum of the system are not conserved separately and a general analytical solution is not possible. The integral has been used to derive numerous solutions in special cases.

Definition

Synodic system

One of the suitable coordinates system used is so called synodic or co-rotating system, placed at the barycentre, with the line connecting the two masses μ<sub>1</sub>, μ<sub>2</sub> chosen as x-axis and the length unit equal to their distance. As the system co-rotates with the two masses, they remain stationary and positioned at (&minus;μ<sub>2</sub>,&nbsp;0) and (+μ<sub>1</sub>,&nbsp;0)<sup>1</sup>.

In the (x,&nbsp;y)-coordinate system, the Jacobi constant is expressed as follows:

<math>C_J=n^2 (x^2+y^2) + 2 left(frac+fracright) - left(dot x^2+dot y^2+dot z^2right)</math>


where:

  • <math>n=frac</math> is the mean motion (orbital period T)
  • <math>mu_1=Gm_1,!,mu_2=Gm_2,!</math>, for the two masses m<sub>1</sub>, m<sub>2</sub> and the gravitational constant&nbsp;G
  • <math>r_1,!,r_2,!</math> are distances of the test particle from the two masses


Note that the Jacobi integral is minus twice...
Read More

No feeds found

All
Posting your question. Please wait!...


No updates available.
No messages found
Suggested Pages
Tell your friends >
about this page
 Create a new Page
for companies, colleges, celebrities or anything you like.Get updates on MyPage.
Create a new Page
 Find your friends
  Find friends on MyPage from