TY - JOUR

T1 - Zero-Velocity Surface in the General Three-Body-Problem

AU - Титов, Владимир Борисович

PY - 2023/3/1

Y1 - 2023/3/1

N2 - The zero-velocity surfaces of the general planar three-body problem are constructed in form space, i.e., the factor space of the configuration space by transfer and rotation. Such a space is the space of congruent triangles, and the sphere in this space is similar triangles. The integral of energy in form space gives the equation of a zero-velocity surface. These surfaces can also be obtained based on the Sundman inequality. Such surfaces separate areas of possible motion from areas where motion is impossible.

AB - The zero-velocity surfaces of the general planar three-body problem are constructed in form space, i.e., the factor space of the configuration space by transfer and rotation. Such a space is the space of congruent triangles, and the sphere in this space is similar triangles. The integral of energy in form space gives the equation of a zero-velocity surface. These surfaces can also be obtained based on the Sundman inequality. Such surfaces separate areas of possible motion from areas where motion is impossible.

KW - general three-body problem

KW - region of permitted motion

KW - zero-velocity surface

UR - https://www.mendeley.com/catalogue/e9625e58-4153-3521-a1c1-59a9d232fd37/

U2 - 10.1134/S1063454123010144

DO - 10.1134/S1063454123010144

M3 - Article

VL - 56

SP - 125

EP - 133

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -