Namespace inertialsim::geometry::power_series¶

Namespace List > inertialsim > geometry > power_series

Public Functions¶

Type	Name
Scalar1D	f1 (const Scalar1D & x) Calculate \(sin(x)/x\).
Scalar1D	f2 (const Scalar1D & x) Calculate \((1-cos(x))/x^2\).
Scalar1D	f3 (const Scalar1D & x) Calculate \((x-sin(x))/x^3\).
Scalar1D	f4 (const Scalar1D & x) Calculate \((0.5\x^2+cos(x)-1)/x^4\).*
Scalar1D	f5 (const Scalar1D & x) Calculate \(1/x^2 - (1+cos(x))/(2\x\sin(x))\).
Scalar1D	fn (const Scalar1D & x) Calculate \((2x-3sin(x)+xcos(x))/(2x^5)\).

Public Functions Documentation¶

function f1¶

Calculate \(sin(x)/x\).

Scalar1D inertialsim::geometry::power_series::f1 (
    const Scalar1D & x
)

Calculation is performed in a stable way as positive x -> 0.0 from above. From above and below, the mathematical limit of this function is 1.0. For small x, the function will use the Taylor series approximation and is designed to maintain at least 10 digits of precision.

Parameters:

x Input angle in radians, x >= 0.

Returns:

result: The value for each input.

function f2¶

Calculate \((1-cos(x))/x^2\).

Scalar1D inertialsim::geometry::power_series::f2 (
    const Scalar1D & x
)

Calculation is performed in a stable way as positive x -> 0.0 from above. From above and below, the mathematical limit of this function is 0.5. For small x, the function will use the Taylor series approximation and is designed to maintain at least 10 digits of precision.

Parameters:

x Input angle in radians, x >= 0.

Returns:

result: The value for each input.

function f3¶

Calculate \((x-sin(x))/x^3\).

Scalar1D inertialsim::geometry::power_series::f3 (
    const Scalar1D & x
)

Calculation is performed in a stable way as positive x -> 0.0 from above. From above and below, the mathematical limit of this function is ⅙. For small x, the function will use the Taylor series approximation and is designed to maintain at least 10 digits of precision.

Parameters:

x Input angle in radians, x >= 0.

Returns:

result: The value for each input.

function f4¶

Calculate \((0.5\*x^2+cos(x)-1)/x^4\).

Scalar1D inertialsim::geometry::power_series::f4 (
    const Scalar1D & x
)

Calculation is performed in a stable way as positive x -> 0.0 from above. From above and below, the mathematical limit of this function is 1/12. For small x, the function will use the Taylor series approximation and is designed to maintain at least 10 digits of precision.

Parameters:

x Input angle in radians, x >= 0.

Returns:

result: The value for each input.

function f5¶

Calculate \(1/x^2 - (1+cos(x))/(2\*x\*sin(x))\).

Scalar1D inertialsim::geometry::power_series::f5 (
    const Scalar1D & x
)

Calculation is performed in a stable way as positive x -> 0.0 from above. From above and below, the mathematical limit of this function is 1/12. For small x, the function will use the Taylor series approximation and is designed to maintain at least 10 digits of precision.

Parameters:

x Input angle in radians, x >= 0.

Returns:

result: The value for each input.

function fn¶

Calculate \((2x-3sin(x)+xcos(x))/(2x^5)\).

Scalar1D inertialsim::geometry::power_series::fn (
    const Scalar1D & x
)

Calculation is performed in a stable way as positive x -> 0.0 from above. From above and below, the mathematical limit of this function is 1/120. For small x, the function will use the Taylor series approximation and is designed to maintain at least 10 digits of precision.

Parameters:

x Input angle in radians, x >= 0.

Returns:

result: The value for each input.

The documentation for this class was generated from the following file cpp/include/inertialsim/geometry/power_series.h