Clinostats are devices designed to simulate microgravity environments by rotating samples along one or more axes, thereby averaging out gravitational forces. This document provides an analytical framework for a dual-axis ideal clinostat, examining its mathematical foundations and operational principles. It outlines the conversion of rotation rates into angular velocities, derives the corresponding rotation matrices, and demonstrates how to combine these matrices to describe the sample's orientation. It further explores how gravitational forces transform in the rotating frame and discusses methods for averaging these forces over time.