The presented work concerns the modelling and stability analysis of 155 mm spin-stabilised projectiles equipped with steering fins. While a large roll rate provides the projectile with interesting stability properties, it also renders the steering control problem very difficult due to the need for very fast fin actuator dynamics. Reciprocally, this control problem can be facilitated by reducing the projectile's roll rate using differential fin steering. This paper presents a technique allowing to assess to what extent roll rate can be reduced without jeopardising trajectory stability. First, a non-linear mathematical model for the considered class of projectiles is presented. This model is then linearised along a reference trajectory, thus, yielding a linear time-varying (LTV) model that can be used to facilitate stability analysis through frozen-time eigenvalue computation. The stability of the projectile's trajectory is then analysed under various, and successively steeper, decreasing roll rate profiles, obtained through two proposed adaptive control schemes for the roll rate channel. The presented stability analysis technique can then be used in order to find a minimum limit for the roll rate, below which the projectile trajectory becomes unstable.