Modelling a uniaxial inerter in a 2D or 3D environment: Implications of centripetal acceleration

•The concept of a uniaxial inerter in a 2D polar coordinate system is proposed.•The theoretical model of a uniaxial inerter expressed with a general vector form in a 3D environment is derived.•The expressions of the proposed inerter model for cartesian and spherical coordinates are derived.•The methodology of implementing a 2D or 3D uniaxial inerter into a multibody system is proposed.•The influence of the centripetal acceleration term in the inerter model is demonstrated using two case studies.