# Chapter1
**URL:** https://liegrouprobotics.discourse.group/c/chapter1/5.md
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## [\[About this category\] Chapter 1 – Why Lie Group Robotics](https://liegrouprobotics.discourse.group/t/about-this-category-chapter-1-why-lie-group-robotics/8)
**Author:** [@lgr\_admin](https://liegrouprobotics.discourse.group/u/lgr_admin)\
**Replies:** 0\
**Last updated:** [July 1, 2025, 6:40am UTC](https://liegrouprobotics.discourse.group/t/about-this-category-chapter-1-why-lie-group-robotics/8 "2025-07-01T06:40:01Z")
Welcome to the discussion category for Chapter 1: Why Lie Group Robotics. This chapter introduces the foundational motivation for using Lie group theory in robotics. Key concepts include: Basic definitions and example…
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## [Chapter 1 - Summary](https://liegrouprobotics.discourse.group/t/chapter-1-summary/35)
**Author:** [@lgr\_admin](https://liegrouprobotics.discourse.group/u/lgr_admin)\
**Replies:** 0\
**Last updated:** [July 11, 2026, 4:07am UTC](https://liegrouprobotics.discourse.group/t/chapter-1-summary/35 "2026-07-11T04:07:24Z")
Summary. The chapter opens by motivating why robotics should be built on Lie groups rather than on conventional parameterizations. Euler angles do not uniquely specify orientation and suffer the gimbal-lock (representat…
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## [Problem & Solution 1.2](https://liegrouprobotics.discourse.group/t/problem-solution-1-2/27)
**Author:** [@lgr\_admin](https://liegrouprobotics.discourse.group/u/lgr_admin)\
**Replies:** 0\
**Last updated:** [August 14, 2025, 4:36am UTC](https://liegrouprobotics.discourse.group/t/problem-solution-1-2/27 "2025-08-14T04:36:40Z")
(Differentials of left and right multiplications) To describe the rigid body motion, we need two coordinate frames: the reference frame and the body frame attached to the movable rigid body (see Figure 1). Assume that t…