How Can We Simplify This Gravitomagnetic Integral?

In summary, to simplify an expression, you need to combine like terms, distribute any numbers or variables, and then perform any necessary operations (such as addition, subtraction, multiplication, or division) from left to right. An example of simplifying an expression is combining the like terms 3x and 2x to get 5x, and then adding the constant 5 to get the simplified expression 5x + 5. The purpose of simplifying an expression is to make it easier to work with and understand, as well as identify patterns or common factors. There are general rules to follow when simplifying an expression, but the specific steps may vary. Additionally, simplifying an expression can change its value as the resulting expression may
  • #1
olgerm
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##m*\frac{G*16*π*ρ*ω}{c^2}*\int_{a_0}^{a_{1}}(da*a*\int_{y}^{H+y} (\int_0^R (\int_0^{2*π} (\frac{(r-a*Cos(α))*r^2}{(a^2+r^2+h^2-2*r(a*Cos(α)))^{3/2}}* dα)dr)dh))##
This equation is related with this post https://www.physicsforums.com/threads/gravitomagnetic-experiment.824048/.

It where helpful if you could simplify even most inner Integral.
 
Last edited:
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  • #2
What did you try?
 
  • #3
The innermost integral is basically A*cos(alpha) / (B + C * cos(alpha)) ^3/2 to be integrated over alpha from 0 to 2pi.

Integral tables may help or you can use u substitution with integration by parts to see if that leads anywhere.
 

FAQ: How Can We Simplify This Gravitomagnetic Integral?

How do I simplify an expression?

To simplify an expression, you need to combine like terms, distribute any numbers or variables, and then perform any necessary operations (such as addition, subtraction, multiplication, or division) from left to right.

Can you give an example of simplifying an expression?

Sure, for example, to simplify the expression 3x + 2x + 5, you would combine the like terms 3x and 2x to get 5x, and then add the constant 5 to get the simplified expression 5x + 5.

What is the purpose of simplifying an expression?

The purpose of simplifying an expression is to make it easier to work with and understand. It also allows you to see the relationship between different terms and identify any patterns or common factors.

Are there any specific rules or steps to follow when simplifying an expression?

Yes, there are some general rules to follow when simplifying an expression, such as combining like terms, following the order of operations, and using the distributive property. However, the specific steps may vary depending on the complexity of the expression.

Can simplifying an expression change its value?

Yes, simplifying an expression can change its value. This is because when you combine like terms or perform operations, the resulting expression may have a different numerical value than the original expression.

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