Donald D. Smith, 55, a former electronics engineer and a mathematician with the Navy Department and then the Johns Hopkins Applied Physics Laboratory, died of cancer Tuesday at Sibley Memorial Hospital.

He had retired from the laboratory in 1975 after undergoing open heart surgery. He joined the laboratory two years earlier and was a mathematician working in communications systems analysis and test and evaluation programs.

Mr. Smith was born in Edgar, Neb. He served in the U.S. Navy from 1941 to 1947, seeing duty in the Pacific during World War II and winning the Silver Star. He was a chief electronics technician's mate.

He then worked as a civilian for the Navy Department here and attended night classes at George Washington University, where he received a degree in mathematics in 1953.

Mr. Smith was an electronics engineer with the Bureau of Ships, the Naval Electronics Systems Command and the Naval Communications Command, all in Washington. He was credited with developing the long range navigation system without significant ambiguities known as OMEGA. He held a letter of commendation from the chief of naval operatons.

He was the author of numerous papers in his field.

He was a member of the International Union of Radio Science and the Toastmasters International.

He is survived by his wife, the former Sarah Grego, and a son, Derek David, of the home in Silver Spring, and a sister, Clarabelle Beale, of Austell, Ga.