Donaldson was born at Cockenzie and Port Seton, Scotland, the son of Captain Peter Donaldson and his wife Mary Dalgleish. Capt. Peter Donaldson sailed regularly on Port Seton Harbour and it is recorded that in 1962, he was on a voyage from Bass Strait Islands with a cargo of livestock, when the vessel Sheerwater was lost off Ninth Island. He and his crew were saved and there are still remains of the ship on the island today. On 31 August 1963, John Donaldson married his first wife, Henrietta Clark Horne, at Port Seton. They emigrated to Tasmania, Australia, in November of that year. Donaldson's parents and his older brother Peter and younger sister Roy also emigrated to Tasmania. His father later worked as a captain for a large maritimetrading company. They had four children, Jane Alison Donaldson, Patricia Anne Donaldson, John Stuart Donaldson and Mary Elizabeth Donaldson, married in 2004 to Frederik, Crown Prince of Denmark. In addition to British citizenship, Donaldson obtained an Australian citizenship in 1975. Henrietta died on 20 November 1997, and Donaldson married Susan Elizabeth Horwood on 5 September 2001. She is a novelist and writes under the names Susan Moody, Susannah James and Susan Madison.
With the marriage of his daughter Crown Princess Mary in 2004, Donaldson was honoured with the Order of the Dannebrog. In accordance with the statutes of the Danish Royal Orders, both he and his daughter were granted a coat of arms, this for display in the Chapel of the Royal Orders at Frederiksborg Castle. The main field of Donaldson's coat of arms is ortinctured and shows a gulesMacDonald eagle and a Sable tinctured boat both symbolising his Scottish ancestry. The chief field is azure tinctured and shows two gold Commonwealth Stars from the Coat of arms of Australia, and a gold infinity symbolin between, symbolising his career as an Australian mathematician. Above the shield is placed a barred helmet topped with a gules rampant lion, which is turned outward. The lion is derived from the Scottish coat of arms and also from the arms of Tasmania and Hobart. The coat of arms of The Crown Princess is almost identical to that of her father's, but a gold rose is depicted as her personal symbol, instead of the infinity symbol. The heraldic crown of a Crown Prince of Denmark is placed above her shield.
Publications
Chick, HL and Collis, KF and Donaldson, JD and Watson, JM, "Professional development in mathematics for teachers: Who, what, why and how", 15th Biennial Conference of the Australian Association of Mathematics Teachers, Darwin, pp. 65–71.
John D. Donaldson and Donald J. Jezewski, "An element formulation for perturbed motion about the center of mass," Celestial Mechanics and Dynamical Astronomy, Volume 16, Number 3.
Michael S. Roberts, John D. Donaldson, and Malcolm Rowland, "Models of hepatic elimination: Comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution, enzyme heterogeneity, and systemic recycling on hepatic elimination," Journal of Pharmacokinetics and Pharmacodynamics, Volume 16, Number 1.
Wotherspoon, SJ and Donaldson, JD, Finite differences and internal tides-representing the boundary, Deep-Sea Research Part I, 43, pp. 949–958. ISSN 0967-0637