Consider the line element of the sphere of radius a: ds²a² (do²+ sin²0 dø²). The only non-vanishing Christoffel symbols are го = − sin 0 cos 0, ФФ ГР = 2.900 rø ГФ00 = ГФ = to reproduce the results written above for rº a) Write down the metric and the inverse metric, and use the definition 1 (8μgvo + dvguo - doguv) = rº vp and r op ΦΘ 00* = 1 tan 0 b) Write down the two components of the geodesic equation. c) The geodesics of the sphere are great circles. Thinking of 0 = 0 as the North pole and = π as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, and also the solution corresponding to the equator.

Consider the line element of the sphere of radius a: ds²a² (do²+ sin²0 dø²). The only non-vanishing Christoffel symbols are го = − sin 0 cos 0, ФФ ГР = 2.900 rø ГФ00 = ГФ = to reproduce the results written above for rº a) Write down the metric and the inverse metric, and use the definition 1 (8μgvo + dvguo - doguv) = rº vp and r op ΦΘ 00* = 1 tan 0 b) Write down the two components of the geodesic equation. c) The geodesics of the sphere are great circles. Thinking of 0 = 0 as the North pole and = π as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, and also the solution corresponding to the equator.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Suppose A = (-2.28 m)i + (4.92 m)j, B = (2.69 m)i + (-3.81 m)j + (1.48 m)k, and D = (-3.56 m)i + (-3.89 m)j. What is the angle in degrees between D and A? What is the angle in degrees between D and B?
The force F is applied 45 degrees counter clockwise from the surface of the slope. The slope is 20 degrees counter clockwise from the horizontal. The magnitude of F is 60lbs. Determine the magnitude of the Force F applies along the slope
c) The geodesics of the sphere are great circles. Thinking of θ = 0 as the North pole and θ = π as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, andalso the solution corresponding to the equator.
In (Figure 1), l = 4 m and n = 4.5 m. Figure 11 B 8 F=600 N 3 m 1 of 1 Part A Determine the angle between the force and the line AB. Express your answer in degrees to three significant figures. 17 ΑΣΦ 0 = Submit Provide Feedback Request Answer vec ?
12.0 B = 5.0 F = 20.0 86400 365) %3D 24 (6)60) = Esc 60° A = 10.0 30 30° 53° D = 20.0 37° Assuming the +x-axis is horizontal to the right for the vectors in the figure, find the following scalar products. a. Ā . B- b. Č - (- 3) - c. Dx F- a. (5 x F) - ( x Ã) -
The length of the slope of a mountain is 2750 m, and it makes an angle of 13.4° with the horizontal. What is the height of the mountain, relative to its base?
Problem 17. For the tree in Problems 13 and 14. knowing the tension in cable AB 13 950 lbs 1bs and the tension in cable AC is 810 lbs. determine the magnitude and direction of the resultant force atA Write the force vector of the resultant A in terms of its unit vectors. 45° 25 40 P.
The ocean is not flat, because the Earth is curved. Take the radius of the Earth to be 6.38 × 103 km. How many meters lower will its surface be 32.0 km from the ship as measured along a line that is tangent to the surface of the Earth at the location of the ship?
solve for the cylindrical and spherical coordinates of vector N=24i-2j+9k and show the illustration of the graph of spherical and cylindrical.
A fox leaves its den and travels 575 yeards west, then 475 yards northwest. In what direction must the fox travel to head directly back to its den? Round your answer to the nearest hundreth. Enter N for North, E for East, W for West, and S for South.
1. Consider two points in space A = (2,1,3) and B = (1,0, – 1), and let a' and b represent the vectors OA and OB , respectively, where O = (0,0,0) is the origin. (a) Find the coordinate of the fourth vertex of the parallelogram whose other three vertices are 0, A, and B. (b) Let c = a' + b, find the unit vectors î, î, and î, in the direction of a', b, and c, respectively. (c) Find the projection of 2 a – 3 b onto the x, y and z axis, respectively. (d) Find the angle between 2 a' – 3 b and the x, y and z axis, respectively.
Consider the 2D vectors A and B. A has a magnitude of 3.5 and a polar angle of 55 degrees, while B has a magnitude of 4.5 and a polar angle of 245 degrees. a) Express A + B in cartesian form. b) Find the magnitude of A + B. c) Find the direction of A + B. d) Express A −B in cartesian form. e) Find the magnitude of A −B. f) Find the direction of A −B. Test 1 Review ProblemsPhysics 30Ad) Express A −B in cartesian form. e) Find the magnitude of A −B.f) Find the direction of A −B.