Distributed Interactive Applications (DIAs) are a class of software that allow geographically remote users to interact within a shared virtual environment. Many DIAs seek to present a rich and realistic virtual world to users, both on a visual and behavioural level. A relatively recent addition to virtual environments (both distributed and single user) to achieve the latter has been the simulation of realistic physical phenomena between objects in the environment. However, the application of physics simulation to virtual environments in DIAs currently lags that of single user environments. This is primarily due to the unavailability of entity state update mechanisms which can maintain consistency in such physics-rich environments. The difference is particularly evident in applications built on a peer-to-peer architecture, as a lack of a single authority presents additional challenges in synchronising the state of shared objects while also presenting a responsive simulation. This thesis proposes a novel state maintenance mechanism for physics-rich environments in peer-to-peer DIAs composed of two parts: a dynamic authority scheme for shared objects, and a physics-aware dead reckoning model with an adaptive error threshold. The first part is intended to place a bound on the overall inconsistency present in shared objects, while the second is implemented to minimise the instantaneous inconsistency during users’ interactions with shared objects. A testbed application is also described, which is used to validate the performance of the proposed mechanism. The state maintenance mechanism is implemented for a single type of physicsaware application, and demonstrates a marked improvement in consistency for that application. However, several flexible terms are described in its implementation, as well as their potential relevance to alternative applications. Finally, it should be noted that the physics-aware dead reckoning model does not depend on the authority scheme, and can therefore be employed with alternative authority schemes