THE potential effects of vigorous exercise on the workings of the female reproductive system have received much attention in recent years. Many of the scares have turned out to be myths. For example, the notion that running may cause the pelvic organs to ''loosen'' and ''drop'' has been discounted as the opposite of what actually happens through exercise, which strengthens the pelvic musculature and gives added support to reproductive organs.

But other concerns have stood the test of careful, detailed research and should be understood by every girl or woman who undertakes vigorous physical activity as well as by the physicians who care for her. No woman or her physician should assume that menstrual irregularity or disruption of a once-normal cycle is due to exercise. Many other causes, some of which require treatment, are possible and should be looked into before concluding that exercise is the reason.

To be sure, exercise has some well-known benefits for the menstruating woman. In most surveys, women who exercise regularly, such as joggers, report that since taking up their activity on a regular basis, they have experienced less premenstrual tension, less menstrual discomfort, shorter periods and less bleeding.

All the facts about the effects of exercise on menstruation are not yet known. A number of studies are currently under way, and it is hoped future research will point to precise causes of the commonly encountered menstrual problems and ways to avoid or correct them without disrupting the woman's exercise program. Meanwhile, here is what is known to date:

Delayed menarche. The average girl in the United States today begins to menstruate between the ages of 12 and 13, although some start earlier and others later. If the menstrual cycle has not begun by age 16, most experts recommend that the girl be thoroughly examined for possible organic or hormonal causes.

Studies at Harvard Medical School and Colorado State University have shown that girls who participate in vigorous athletic training, such as ballet dancers and swimmers, commonly experience a delay in menarche (pronounced men-AR-kee), as attaining the first menstrual period is called. Another name for delayed menarche is primary amenorrhea, which means no periods in a woman who never had periods. One Harvard study by Dr. Rose E. Frisch and colleagues revealed that 10 percent of ballet dancers who had reached the age of 18 1/2 had not yet begun to menstruate. On average, among those whose periods had begun, rigorous ballet training delayed menarche by about one year.