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RollPitchYawAngles[r]

给出与旋转矩阵 r 相一致的滚动-俯仰-偏航角 {α,β,γ}.

RollPitchYawAngles[r,{a,b,c}]

给处于旋转顺序 {a,b,c} 相一致的滚动-俯仰-偏航角 {α,β,γ}.

更多信息
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范例  
基本范例  
范围  
属性和关系  
可能存在的问题  
参见
相关指南
历史
按以下格式引用：

RollPitchYawAngles

RollPitchYawAngles[r]

给出与旋转矩阵 r 相一致的滚动-俯仰-偏航角 {α,β,γ}.

RollPitchYawAngles[r,{a,b,c}]

给处于旋转顺序 {a,b,c} 相一致的滚动-俯仰-偏航角 {α,β,γ}.

更多信息

  • RollPitchYawAngles 用于分解轴朝向固定的旋转.
  • RollPitchYawAngles[r,{a,b,c}] 给出角 {α,β,γ} 使得 RollPitchYawMatrix[{α,β,γ},{a,b,c}]r.
  • RollPitchYawAngles[r] 等价于 RollPitchYawAngles[r,{3,2,1}]， z-y-x 旋转.
  • 默认的 z-y-x 角 RollPitchYawAngles[r,{3,2,1}] 把旋转分解成三步：
  • 旋转轴 a、b 和 c 和可以是任意整数 1、2 或 3，但只有12种组合足够普适，可用于指定任意三维旋转.
  • 第一个和最后一个轴重复的旋转：
  • {3,2,3}z-y-z 旋转
    {3,1,3}z-x-z 旋转
    {2,3,2}y-z-y 旋转
    {2,1,2}y-x-y 旋转
    {1,3,1}x-z-x 旋转
    {1,2,1}x-y-x 旋转
  • 三个轴都不同的旋转：
  • {1,2,3}x-y-z 旋转
    {1,3,2}x-z-y 旋转
    {2,1,3}y-x-z 旋转
    {2,3,1}y-z-x 旋转
    {3,1,2}z-x-y 旋转
    {3,2,1}z-y-x 旋转 (默认)
  • 后续轴重复的旋转可能不可逆，因为它们不能表示三维中所有的旋转.

范例

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基本范例  (2)

从旋转矩阵中获取滚动-俯仰-偏航角：

Wolfram Language code: m = RollPitchYawMatrix[{Pi / 4, Pi / 2, 0}];
Wolfram Language code: RollPitchYawAngles[m]

从有给定旋转顺序的旋转矩阵中获取滚动-俯仰-偏航角：

Wolfram Language code: m = RollPitchYawMatrix[{Pi / 2, Pi / 3, Pi / 4}, {1, 2, 3}];
Wolfram Language code: RollPitchYawAngles[m, {1, 2, 3}]

范围  (2)

从旋转矩阵中获取滚动-俯仰-偏航角：

Wolfram Language code: m = RollPitchYawMatrix[{Pi / 7, Pi / 3, Pi / 3}];
Wolfram Language code: RollPitchYawAngles[m, {3, 2, 1}]

从有给定旋转顺序的旋转矩阵中获取滚动-俯仰-偏航角：

Wolfram Language code: m = RollPitchYawMatrix[{Pi / 2, Pi / 3, Pi / 4}, {1, 2, 3}];
Wolfram Language code: RollPitchYawAngles[m, {1, 2, 3}]

属性和关系  (1)

RollPitchYawAngles 返回 RollPitchYawMatrix 给出相同旋转矩阵的角度：

Wolfram Language code: m1 = RollPitchYawMatrix[{π / 3, π / 2, π / 4}]; m2 = RollPitchYawMatrix[RollPitchYawAngles[m1]];
Wolfram Language code: m1 == m2

角度不必是相同的：

Wolfram Language code: a1 = {π / 2, π, π / 3}; m1 = RollPitchYawMatrix[a1];
Wolfram Language code: a2 = RollPitchYawAngles[m1]

但是两组角度产生的是相同的旋转矩阵：

Wolfram Language code: RollPitchYawMatrix[a1] == RollPitchYawMatrix[a2]

可能存在的问题  (1)

RollPitchYawMatrix 允许连续的轴相等，这就生成了一个旋转矩阵：

Wolfram Language code: m = RollPitchYawMatrix[{Pi, Pi / 2, Pi / 8}, {1, 1, 2}]
Wolfram Language code: {OrthogonalMatrixQ[m], Det[m]}//Simplify

但是 RollPitchYawAngles 要求连续的轴是不同的：

Wolfram Language code: RollPitchYawAngles[m, {1, 1, 2}]

这是因为连续的轴相等的话，有些旋转矩阵可能无法表示：

Wolfram Language code: m1 = RollPitchYawMatrix[{Pi / 3, 0, 0}, {3, 2, 1}]
Wolfram Language code: m2 = RollPitchYawMatrix[{α, β, γ}, {1, 1, 2}]
Wolfram Language code: FindInstance[And@@Thread[m1 == m2], {α, β, γ}]
Wolfram Research (2015)，RollPitchYawAngles，Wolfram 语言函数，https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.

文本

Wolfram Research (2015)，RollPitchYawAngles，Wolfram 语言函数，https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.

CMS

Wolfram 语言. 2015. "RollPitchYawAngles." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.

APA

Wolfram 语言. (2015). RollPitchYawAngles. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/RollPitchYawAngles.html 年

BibTeX

@misc{reference.wolfram_2026_rollpitchyawangles, author="Wolfram Research", title="{RollPitchYawAngles}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/RollPitchYawAngles.html}", note=[Accessed: 16-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_rollpitchyawangles, organization={Wolfram Research}, title={RollPitchYawAngles}, year={2015}, url={https://reference.wolfram.com/language/ref/RollPitchYawAngles.html}, note=[Accessed: 16-August-2026]}