Relativity: Differential Geometry
Not what you're looking for?
A particle moves along a parametrized curve given by
x(lamda)=cos(lamda), y(lamda)=sin(lamda), z(lamda)=lamda
Express the path of the curve in the spherical polar coordinates {r, theta, pheta}
where x = rsin(theta)cos(pheta)
y=rsin(theta)sin(pheta)
z=rcos(theta)
so that the metric is
ds^2=dr^2+(r^2)d(theta)^2+(r^2)sin^2(theta)d(pheta)^2
Calculate the components of the tangent vector to the curve in both Cartesian and spherical polar coordinate systems.
Purchase this Solution
Solution Summary
This solution shows step-by-step calculations to express the path of the curve in the specific spherical polar coordinates and also determines the components of the tangent vector to the curve in both Cartesian and spherical polar coordinates. All workings and formulas are shown in a clear and structured manner.
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts