Physics-based digital twins for heavy equipment provide a powerful tool for improving operation and maintenance activities. In contrast to data-driven models, they present more explainable and confident results but require more computational power. Besides the problem of physics-based digital twins creation, there is a task of managing their lifecycle, including their execution, maintenance, storage, and updating. The features distinguishing this kind of digital twins are the mobility of the real counterpart, operation in remote locations, long lifecycle, information sensitivity, and gaps in information technology awareness among the equipment owners and users. This paper presents a methodology and reference architecture for a set of interconnected systems capable of running digital twins of heavy equipment in such conditions. A data model for preserving digital twin-related information for decades of machine operation is described. Operating-system-level virtualization technologies are used to run digital twins in a heterogeneous execution environment. An example of the reference architecture implementation is presented for the physics-based digital twins of a mobile log crane. The experimental part of the paper includes a comparison of computing time for different types of digital twins in different execution environments. It highlights the peculiarities related to running physics-based digital twins in containers. Experiments were performed using the Amazon cloud platform, an edge computing system represented by a single-board microcomputer based on ARM architecture, and a virtual machine on a desktop personal computer. Experimental results show that physics-based digital twins for the analysis of the multi-body dynamics can be run within the proposed architecture with real-time performance in all three types of execution environments. The paper demonstrates the practical implementation of physics-based digital twins for heavy equipment and defines directions for future research in this field.