Curvilinear Abscissa - Definition & Meaning

Thread starter fishingspree2
Start date Feb 21, 2010
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Curvilinear

In summary, Curvilinear abscissa is the distance measured along a curved line or curve, while linear abscissa is the distance measured along a straight line. It is commonly used in mathematics, physics, engineering, and architecture for various applications such as measuring the distance traveled along a curved path and drawing curved lines and structures. The calculation of curvilinear abscissa involves finding the integral of the curve's equation between two given points using calculus or numerical methods. In calculus, it is used to calculate the length of a curve and is important in finding the area under a curve and solving optimization problems. It is also used in the study of parametric curves and polar coordinates.

Feb 21, 2010

fishingspree2

Hello,

what does curvilinear abscissa mean?

thank you

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Feb 21, 2010

tiny-tim

Science Advisor

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Hello fishingspree2!

I think it just means that you use a curvilinear grid instead of the usual rectangular Cartesian grid …

you follow the line down to the "axis" in the same way that you'd usually follow a straight line to the x-axis to get the usual abcissa (x-coordinate).

1. What is the definition of Curvilinear Abscissa?

Curvilinear abscissa refers to the distance measured along a curved line or curve, from a fixed point to another point on the curve.

2. How is Curvilinear Abscissa different from Linear Abscissa?

Linear abscissa is the distance measured along a straight line, while curvilinear abscissa is the distance measured along a curved line or curve. This means that the direction and shape of the line or curve will affect the measurement of the abscissa.

3. What are some real-world applications of Curvilinear Abscissa?

Curvilinear abscissa is commonly used in mathematics and physics to measure the distance traveled along a curved path, such as the trajectory of a projectile or the path of a moving object. It is also used in engineering and architecture for drawing and measuring curved lines and structures.

4. How is Curvilinear Abscissa calculated?

The calculation of curvilinear abscissa involves finding the integral of the curve's equation between two given points. This can be done using calculus or numerical methods, depending on the complexity of the curve.

5. What is the significance of Curvilinear Abscissa in calculus?

In calculus, curvilinear abscissa is used to calculate the length of a curve, which is an important concept in finding the area under a curve and in solving various optimization problems. It is also used in the study of parametric curves and polar coordinates.