# Derek Frank Lawden

(1919–2008)

#### ScD *Cantab* FIMA FRSNZ

**DEREK LAWDEN** was born in Birmingham, UK, on 15th September 1919 and died in Warwick, UK, on 15th February 2008. He attended King Edward VI Grammar School, Aston and won a scholarship to Cambridge to study Mathematics. He graduated in 1947 as a Wrangler in the Tripos examinations. He served as a captain in the Royal Artillery from 1939 until 1946, for a time being in charge of coast artillery radar at Gibraltar. After leaving the army he was appointed a lecturer in mathematics at the Royal Military College of Science, researching in control systems. Later, he moved to the College of Advanced Technology Birmingham, where he began work on the theory of optimal rocket trajectories.

In 1956 he was appointed Professor of Mathematics at the University of Canterbury, New Zealand. At that time the department had a total staff of just five, including one chair. Appointment to this chair automatically meant being Head of Mathematics, including pure and applied mathematics, and statistics.

Derek's arrival had an immediate and stimulating effect on the department, through his energy and his refreshing ideas on teaching and research. He reformed and modernized the prescriptions of most of the courses. He was keen to foster a commitment to research and was already strongly involved himself, having published several papers on the optimization of rocket trajectories, particularly in applications to interplanetary travel. He made significant contributions in this field, which had become the subject of intense research in the United States, that country having already committed itself to sending a man to the moon. This resulted in appointments as a consultant to such companies as Boeing and Lockheed, which led to several visits to the USA. These contacts were eventually terminated because of his opposition to the war in Vietnam. All this work culminated in a text-book, 'Optimal Trajectories for Space Navigation' published in 1963.

The quality of his research led to several high awards: the Sc.D. degree by Cambridge University (1962), a Fellowship of the Royal Society of New Zealand (1962), the Society's Hector Medal (1964) and the Mechanics and Control of Flight Award of the American Institute of Aeronautics and Astronautics (1967). He was unable to receive the last of these in person, his visa having been cancelled by the US government.

Derek was certainly inclined towards applied mathematics, rather than to the more abstract topics of pure mathematics. This shows in his choice of subject matter for his books. He believed in the importance of establishing a sound, coherent mathematical framework for any applied topic, based on a careful interpretation of known observational facts. However, he was very ready to make use of advanced results from pure mathematics if need be, such as in the field of differential equations.

Socially Derek was a witty, entertaining and provocative conversationalist and public speaker, often expressing an unconventional viewpoint. For example, early in life he espoused the views of the British Interplanetary Society, at a time when these were frequently derided, and he became a member of the New Zealand Rationalist Association.

He enjoyed playing bridge, and his founding of the University bridge club gave a real lift to the social life of the university.

In his eleven years in New Zealand he contributed much, in various ways. When he announced that he would be returning to England with his family in 1967, the news was received with a feeling of real regret by the mathematical community throughout New Zealand and by many others, especially in Christchurch. He made it clear that he had enjoyed his time in New Zealand, and that it was for family reasons that he was returning to England.

He took up the position of Professor of Mathematical Physics at the University of Aston in Birmingham and was appointed Head of Mathematics in 1977. He retired from this post in 1983 and, after a short spell as a visiting professor at the University of Natal in South Africa, moved to the country, where he wrote a series of books on topics from mathematical physics, several of which have been reprinted as Dover editions.

Apart from mathematics, he had a life-long interest in psychical research, believing that consciousness was the missing link in our scientific understanding of the universe. He had a strong moral sense which, in his early life, drew him towards left-wing idealism. However, he eventually became deeply disillusioned with it because of its toxic practical effects, particularly with what he regarded as the harmful effect of egalitarianism on standards in education. His views on this were influenced by his gratitude for his grammar school education, which he considered had given him his chance in life. Although his views changed, he always expressed them with force and clarity, and scorned the obscurantist, opaque language used in modern academia.

He leaves three sons and a widow.

## Bibliography

### Books

- Lawden, D. F. 1954: Mathematics of Engineering Systems, Methuen. 404pp.
- Lawden, D. F. A. 1960: A Course in Applied Mathematics, English Universities Press, London. 655pp.
- Lawden, D. F. 1962: An Introduction to Tensor Calculus and Relativity, Methuen. 186pp.
- Lawden, D. F. 1963: Optimal Trajectories for Space Navigation, Butterworths. 126pp.
- Lawden, D. F. 1967: The Mathematical Principles of Quantum Mechanics, Methuen. 280pp.
- Lawden, D. F. 1972: Analytical Mechanics, Allen & Unwin. 78pp.
- Lawden, D. F. 1973: Electromagnetism, Allen & Unwin. 96pp.
- Lawden, D. F. 1975: Analytical Methods of Optimization, Scottish Academic Press, Edinburgh. 157pp.
- Lawden, D. F. 1985: Elements of Relativity Theory, Wiley. 108pp.
- Lawden, D. F. 1987: Principles of Thermodynamics and Statistical Mechanics, Wiley. 154pp.
- Lawden, D. F. 1989: Elliptic Functions and Applications, Springer-Verlag. 334pp.

### Published Papers

#### Psychical Research

- Lawden, D. F. 1979: On a Poltergeist Case.
*Journal of The Society for Psychical Research 50*. No. 780. - Lawden, D. F. 1989: Some Thoughts on Birth and Death.
*Journal of Psychophysical Systems*, October.

#### Philosophical Research

- Lawden, D. F. 1964: Chemical Evolution + Origin of Life.
*Nature 202*: 412 - Lawden, D. F. 1965: The Rise of the Concept of a Physical Model.
*Transactions of the Royal Society of New Zealand 1*: 161-174. - Lawden, D. F. 1968: Modelling Physical Reality.
*Philosophical Journal 5, No 2*. - Lawden, D. F. 1969: Are Robots Conscious?
*New Scientist 43: No 6*. - Lawden, D. F. 1972: Towards a Non-Behavioural Psychology.
*Philosophical Journal 9*: 116-124. - Lawden, D. F. 1983: Alternate Culture.
*Nature 301*: 9.

#### Mathematical Research

- Lawden, D. F. 1951a: A General Theory of Sampling Servo Systems.
*Institution of Electrical Engineers 98*: 31-36. - Lawden, D. F. 1951b: Entry into Circular Orbits. 1.
*Journal of the British Interplanetary Society 10*, No. 1. - Lawden, D. F. 1951c: The Function Infinity-igma-n=1nrzn and Associated Polynomials.
*Proceedings of the Cambridge Philosophical Society 47*: 309-314. - Lawden, D. F. 1952a: Inter-Orbital Transfer of a Rocket.
*Annual Report of The British Interplanetary Society*. - Lawden, D. F. 1952b: The Determination of Minimal Orbits.
*Journal of The British Interplanetary Society 11*, No. 5. - Lawden, D. F. 1952c: Orbital Transfer via Tangential Ellipses.
*Journal of The British Interplanetary Society 11*, No. 6. - Lawden, D. F. 1952d: On the Solution of Linear Difference Equations.
*Mathematical Gazette 36*, No. 317. - Lawden, D. F. 1953a: Minimal Rocket Trajectories.
*Journal of the American Rocket Society 23*: 360-382. - Lawden, D. F. 1953b: Escape to Infinity from Circular Orbits.
*Journal of The British Interplanetary Society 12*: No 2. - Lawden, D. F. 1954a: Entry into Circular Orbits - 2.
*Journal of The British Interplanetary Society 13,*No. 1. - Lawden, D. F. 1954b: Fundamentals of Space Navigation.
*Journal of The British Interplanetary Society 13*, No. 2. - Lawden, D. F. 1954c: Correction of Interplanetary Orbits.
*Journal of The British Interplanetary Society 13*, No. 4. - Lawden, D. F. 1954d: Perturbation Manoeuvres.
*Journal of The British Interplanetary Society 13*, No. 6 - Lawden, D. F. 1954e: Stationary Rocket Trajectories.
*Quarterly Journal of Mechanics and Applied Mathematics 7*: 488-504. - Lawden, D. F. 1954f: Comment on Satellite Orbits for Interplanetary Flight.
*Jet Propulsion 24*: 382-382. - Lawden, D. F. 1955a: Dynamic Problems of Interplanetary Flight.
*Aeronautical Quarterly 6*: 165-180. - Lawden, D. F. 1955b: Optimal Transfer Between Circular Orbits About Two Planets.
*Astronautica Acta 1*, No. 2. - Lawden, D. F. 1955c: Optimum Launching of a Rocket into an Orbit about the Earth.
*Astronautica Acta 1*, No. 4. - Lawden, D. F. 1955d: Optimal Programming of Rocket Thrust Direction.
*Astronautica Acta 1*, No. 6. - Lawden, D. F. 1956a: Maximum Ranges of Intercontinental Missiles.
*Aeronautical Quarterly 8*: 269-278. - Lawden, D. F. 1956b: Transfer Between Circular Orbits.
*Jet Propulsion 26*: 555-558. - Lawden, D. F. 1957a: The Simulation of Gravity.
*Journal of The British Interplanetary Society 6*, No. 3. - Lawden, D. F. 1957b: Mathematical Problems of Astronautics.
*Mathematical Gazette 41*, No. 337. - Lawden, D. F. 1957c: Optimal Rocket Trajectories.
*Jet Propulsion 27*: 1263-1263. - Lawden, D. F. 1958a: Optimal Escape from a Circular Orbit.
*Astronautica Acta 4*, No. 3. - Lawden, D. F. 1958b: Escape from a Circular Orbit Using Tangential Thrust.
*Jet Propulsion, March*. - Lawden, D. F. 1958c: The Employment of Aerodynamic Forces to obtain Maximum Range of a Rocket Missile.
*Aeronautical Quarterly 9*: 97-109. - Lawden, D. F. 1959a: Discontinuous Solutions of Variational Problems.
*Journal of the Australian Mathematical Society 1*, No 1. - Lawden, D. F. 1959b: Necessary Conditions for Optimal Rocket Trajectories.
*Quarterly Journal of Mechanics and Applied Mathematics 12*, No. 4. - Lawden, D. F. 1960a: Optimal Transfer Between Circular Orbits About Two Planets.
*Astronautica Acta 1*, No. 2. - Lawden, D. F.; Long, R. S. 1960: The Theory of Correctional Manoeuvres in Interplanetary Space.
*Astronautica Acta 6*, No. 1. - Lawden, D. F. 1960b: Optimal Programme for Correctional Manoeuvres.
*Astronautica Acta 6*, No. 4. - Lawden, D. F. 1961a: Optimal Powered Arcs in an Inverse Square Law Field.
*American Rocket Society 31*: 566-568. - Lawden, D. F. 1961b: Optimal Intermediate-Thrust Arcs in a Gravitational Field.
*Astronautica Acta 8*, No. 2-3. - Lawden, D. F. 1963: Analytical Techniques for the Optimization of Rocket Trajectories.
*Aeronautical Quarterly 14*: 105-124. - Lawden, D. F. 1965: Celestial Mechanics and Astrodynamics:
*Journal of the Royal Aeronautical Society 69*. - Lawden, D. F. 1968: Coordinate and Momentum Representations in Quantum Mechanics.
*Journal of the Australian Mathematical Society 8*, No. 2. - Lawden, D. F. 1969: Electro-Chemical Dissolution of an Anode.
*Journal of the Australian Mathematical Society 10*, No. 34. - Lawden, D. F. 1970: The Phenomenon of Time Dilation.
*Spaceflight. 12*: 178-179. - Lawden, D. F. 1971: The Phenomenon of Time Dilation.
*Spaceflight. 13*. - Lawden, D. F. 1984: Pseudo-Random Sequence Loops.
*Mathematical Gazette 68*: 39-41. - Lawden, D. F. 1991: Rocket Trajectory Optimization: 1950-1963.
*Journal of Guidance, Control, and Dynamics 14*: 705-711. - Lawden, D. F. 1992a: Optimal Transfers Between Coplanar Elliptic Orbits.
*Journal of Guidance, Control, and Dynamics 15*: 788-791. - Lawden, D. F. 1992b: Calculation of Singular Extremal Rocket Trajectories.
*Journal of Guidance, Control, and Dynamics 15*: 1361-1365. - Lawden, D. F. 1993: Time-Closed Optimal Transfer by 2 Impulses Between Coplanar Elliptic Orbits.
*Journal of Guidance, Control, and Dynamics 16*: 585-587. - Lawden, D. F. 1999: Families of ovals and their orthogonal trajectories.
*Mathematical Gazette 83*, No. 498. - Lawden, D. F. 2000: Touching hyperspheres.
*Mathematical Gazette 84*, No. 499.

*Michael Lawden*

Senior Scientific Officer (Retired)

Starlink Project

Rutherford Appleton Laboratory

UK

*Robert Long*

Reader in Mathematics (Retired)

University of Canterbury

Christchurch

New Zealand