For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from [1], which band together separately sq...For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from [1], which band together separately squared mutual distances between bodies (mass points) and squared distances from bodies to the barycenter of the system. In this case, we prove the Lagrange stability theorem, which allows us to define more exactly the character of hyperbolic-elliptic and parabolic-elliptic final evolutions.展开更多
In keeping with a view that is explicitly formulated by Aristotle in his Motion of Animals, general kinetic principles must be specified according to the different types of movable entities existing in the universe. A...In keeping with a view that is explicitly formulated by Aristotle in his Motion of Animals, general kinetic principles must be specified according to the different types of movable entities existing in the universe. At issue, essentially, are the motions of the stars and the motions of animals. Whereas the cosmological immovable mover is the object of two complementary analyses （in Bk. Ⅷ of Physics and in Chs. 6 and 7 of Bk. Ⅻ of Metaphysics）, information on the immovability of the first mover responsible for animal motion is to be found in the psychological and psycho-physiological treatises （On the Soul, in Bk. Ⅰ, Chs. 3 and 4, and in Bk. Ⅲ, Ch. 10 and in Ch. 6 of the Motion of Animals）. But it is also found in Ch. 7, Bk. Ⅻ of the Metaphysics, in the very context of the argument concerning the absolutely first immovable mover of the world. This suggests that the two types of motion, that of the stars and that of animals, however distinct the arguments about them are, rest on a single scheme, and maybe even on a common principle. This is liable to surprise us, as much as stars and animals appear to us to belong to heterogeneous orders of reality. But the situation is different for Aristotle, who, as attentive as he is to differences, tends nonetheless to conceive the stars as living things of a particular kind. This fact is the source of a series of difficulties that Aristotle generously left for his many commentators to solve. Aim of this text, which was initially directed to a larger audience, is to set some of these complex issues in both simple and up to date terms.展开更多
文摘For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from [1], which band together separately squared mutual distances between bodies (mass points) and squared distances from bodies to the barycenter of the system. In this case, we prove the Lagrange stability theorem, which allows us to define more exactly the character of hyperbolic-elliptic and parabolic-elliptic final evolutions.
文摘In keeping with a view that is explicitly formulated by Aristotle in his Motion of Animals, general kinetic principles must be specified according to the different types of movable entities existing in the universe. At issue, essentially, are the motions of the stars and the motions of animals. Whereas the cosmological immovable mover is the object of two complementary analyses （in Bk. Ⅷ of Physics and in Chs. 6 and 7 of Bk. Ⅻ of Metaphysics）, information on the immovability of the first mover responsible for animal motion is to be found in the psychological and psycho-physiological treatises （On the Soul, in Bk. Ⅰ, Chs. 3 and 4, and in Bk. Ⅲ, Ch. 10 and in Ch. 6 of the Motion of Animals）. But it is also found in Ch. 7, Bk. Ⅻ of the Metaphysics, in the very context of the argument concerning the absolutely first immovable mover of the world. This suggests that the two types of motion, that of the stars and that of animals, however distinct the arguments about them are, rest on a single scheme, and maybe even on a common principle. This is liable to surprise us, as much as stars and animals appear to us to belong to heterogeneous orders of reality. But the situation is different for Aristotle, who, as attentive as he is to differences, tends nonetheless to conceive the stars as living things of a particular kind. This fact is the source of a series of difficulties that Aristotle generously left for his many commentators to solve. Aim of this text, which was initially directed to a larger audience, is to set some of these complex issues in both simple and up to date terms.
