Burnback analysis is a geometric exercise, whose correct solution leads to obtaining the thrust curve of solid propellant rockets. Traditionally, Piobert statement, which introduces a certain amount of intuition, is used as an argument to construct analytical and numerical algorithms, although it is also common to use numerical integration of differential equations, whose solution is free of ambiguities. This paper presents a detailed study of the process experienced by the combustion surface that allows enunciating the properties of the kinematics of the surface without the need to appeal to heuristic considerations. Next, the methods used throughout the technological development of solid propellant rockets are reviewed, from their beginnings to modern methods, which obtain solutions to complex problems, based on the numerical solution of PDE. Other methods are also reviewed, which are developed around some of the properties presented by the solution, that is, methods of heuristic or phenomenological foundation. As a result of the review, it becomes clear that the solution of the Eikonal equation for burnback analysis is undertaken in the early 2000, clarifying the problem. Finally, several examples of the capabilities of the most relevant methods are provided, from the point of view of both efficiency and precision, presenting results in situations of interest, in the field of propulsion by solid-propellant rockets.

翻译：燃面退移分析是一种几何计算问题，其正确解可用于获取固体推进剂火箭的推力曲线。传统上，人们采用引入一定直觉的皮奥伯特表述作为构建解析与数值算法的依据，但微分方程数值积分方法因无歧义性也常被使用。本文详细研究了燃烧表面演化过程，在不依赖启发性假设的前提下阐明了表面运动学特性。随后系统回顾了固体推进剂火箭技术发展历程中采用的各种方法——从早期方法到基于偏微分方程数值求解的现代复杂问题求解技术。此外，还评述了基于解呈现的某些特性而构建的启发式或现象学方法。通过综述可知，21世纪初开始采用程函方程求解燃面退移分析问题，这使问题本质得以澄清。最后从计算效率和精度两个维度，通过展示典型工程场景下的计算结果，验证了主流方法的能力。