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Modeling languages that are used to capture the essential properties of embedded real-time computer systems must also allow a description of the system's physical environment. The reason is that the environment is the ultimate source of all requirements on the system, and in particular, real-time constraints are derived from the dynamics of the physical objects under control. However, most modeling languages, including the object-oriented ones, are not well equipped to describe the continuous-time relationships that exist in the real world. This paper shows how the Unified Modeling Language can be extended to include such modeling, thereby improving the design of embedded systems described in the same language. A realistic case study is elaborated to show the practical usefulness of the results.