Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic

Igor Lukacevic wrote:
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic
If the application is field theory, as opposed to ship navigation, it
might be helpful to look at what we are trying to represent.
http://web.mit.edu/8.02t/www/802TEAL...ttract_100.jpg
From:
http://web.mit.edu/8.02t/www/802TEAL...tics/index.htm
http://vishnu.mth.uct.ac.za/omei/gr/chap6/node8.html

Sue...

If the application is field theory, as opposed to ship navigation, it
might be helpful to look at what we are trying to represent.
http://web.mit.edu/8.02t/www/802TEAL...ttract_100.jpg
From:
http://web.mit.edu/8.02t/www/802TEAL...tics/index.htm
http://vishnu.mth.uct.ac.za/omei/gr/chap6/node8.html

Sue...

No, its application is just an exercise for the undergraduate students.
Unfortunately, link didn't help me. But thnx anyway

I. Lukacevic

Sue... wrote:
Igor Lukacevic wrote:
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic
If the application is field theory, as opposed to ship navigation, it
might be helpful to look at what we are trying to represent.
http://web.mit.edu/8.02t/www/802TEAL...ttract_100.jpg
From:
http://web.mit.edu/8.02t/www/802TEAL...tics/index.htm

I understand the point of these, since the Earth's magnetic field
follows the curvature of its surface.

But why have you included this ...?

http://vishnu.mth.uct.ac.za/omei/gr/chap6/node8.html

Sue...

Mahmoud In My Dinner Jacket wrote:
Sue... wrote:
Igor Lukacevic wrote:
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic
If the application is field theory, as opposed to ship navigation, it
might be helpful to look at what we are trying to represent.
http://web.mit.edu/8.02t/www/802TEAL...ttract_100.jpg
From:
http://web.mit.edu/8.02t/www/802TEAL...tics/index.htm

I understand the point of these, since the Earth's magnetic field
follows the curvature of its surface.

But why have you included this ...?
That gives the question some standing in this NG.

Physics \Phys"ics\, n. [See Physic.]
The science of nature, or of natural objects; that branch of
science which treats of the laws and properties of matter,
and the forces acting upon it; especially, that department of
natural science which treats of the causes (as gravitation,
heat, light, magnetism, electricity, etc.) that modify the
general properties of bodies; natural philosophy.

http://dict.die.net/physics/

Sue...


http://vishnu.mth.uct.ac.za/omei/gr/chap6/node8.html

Sue...

"Igor Lukacevic" wrote in message
news
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic

Ok, just a hint. There is only one parallel that is a great circle,
the equator. Meridians are all great circles. The shortest distance
between Athens, Greece and Fairbanks, Alaska is a great circle.
Which way would an airline pilot go to save fuel?

(Watch out for Sue. One-track mind. )
"That fellow seems to me to possess but one idea, and that is a wrong
one."--Dr. Samuel Johnson

Androcles.

Black Knight wrote:
"Igor Lukacevic" wrote in message
news
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic

Ok, just a hint. There is only one parallel that is a great circle,
the equator. Meridians are all great circles. The shortest distance
between Athens, Greece and Fairbanks, Alaska is a great circle.
Which way would an airline pilot go to save fuel?

(Watch out for Sue. One-track mind. )
"It's clearly a budget. It's got a lot of numbers in it."--Rueters, May
5, 2000
;-)

"That fellow seems to me to possess but one idea, and that is a wrong
one."--Dr. Samuel Johnson

Androcles.

"Igor Lukacevic" wrote in message news
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Meridians have equation
{ theta = x^1 = s
{ phi = x^2 = k (some constant)

(with parallels it's the other way around)

So you have calculated the non-zero Christoffels
{^1_2_2}, {^2_1_2} and {^2_2_1}

So calculate
d theta / ds = 1
d^2 theta / ds^2 = 0
and
d phi /ds = 0
d^2 phi / ds^2 = 0
and verify the geodesics equation. You don't even need the
exact values of the Christoffels for this :-)

Dirk Vdm

I've got the .pdf and now I get it.
I want to thank You all for Your help, especially David and Dirk.

Thanks again

I. Lukacevic

Sue... wrote:
Mahmoud In My Dinner Jacket wrote:
Sue... wrote:
Igor Lukacevic wrote:
Hullo everyone!

I am new to this newsgroup, and to the subject. I have an exercise to
solve, I'm sure it's a simple one, but I just cannot get it right.

I have to prove that meridians on the surface of Earth are geodesics using
the definition of geodesics:

d^2x^i i dx^j dx^k
-------- + { }*-----*------ = 0
ds^2 j k ds ds

I have succeded at proving that parallels are not, but meridians are
giving me trouble. I have calculated Crist. symbols for i,j,k=1,2.

Please, if anyone could help, I would be most gratefull

I. Lukacevic
If the application is field theory, as opposed to ship navigation, it
might be helpful to look at what we are trying to represent.
http://web.mit.edu/8.02t/www/802TEAL...ttract_100.jpg
From:
http://web.mit.edu/8.02t/www/802TEAL...tics/index.htm

I understand the point of these, since the Earth's magnetic field
follows the curvature of its surface.

But why have you included this ...?
That gives the question some standing in this NG.

Physics \Phys"ics\, n. [See Physic.]
The science of nature, or of natural objects; that branch of
science which treats of the laws and properties of matter,
and the forces acting upon it; especially, that department of
natural science which treats of the causes (as gravitation,
heat, light, magnetism, electricity, etc.) that modify the
general properties of bodies; natural philosophy.

http://dict.die.net/physics/

Sue...

No kidding! How long have they been at this physics lark, then?