Solution to problem 18.1.2 from the collection of Kepe O.E.

18.1.2 Material points 1 and 2 move in space. A connection is imposed on material point 1, the equation of which is written as x2 + y2 + z2 - 25 = 0. The connection imposed on point 2 has the form x2 + y2 + z2 - 25 t2 ≤ 0. It is necessary to determine the number of the point on which the holonomic unrestrained connection. (Answer 2)

A holonomic connection is a connection that can only be expressed through the coordinates and time parameters of the system. In this case, a holonomic non-containing constraint is imposed on point 2, since its equation depends only on the coordinate and time. As a result, the answer to the problem is point 2.

Solution to problem 18.1.2 from the collection of Kepe O.?.

The digital product is a solution to problem 18.1.2 from the collection of Kepe O.?. in physics. This product is intended for students and teachers solving problems in this area.

Solving a problem includes a description of the problem conditions, a step-by-step solution and an answer. Problem 18.1.2 describes the movement of material points in space to which connections are imposed. It is necessary to determine the number of the point on which the holonomic non-containing constraint is imposed.

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The digital product is a solution to problem 18.1.2 from the collection of Kepe O.?. in physics. The problem describes the movement of two material points in space, on which connections are imposed. The coupling equation for point 1 has the form x2 + y2 + z2 - 25 = 0, and for point 2 - x2 + y2 + z2 - 25 t2 ≤ 0. Holonomic coupling is a coupling that can only be expressed through the coordinates and time parameters of the system . In this case, a holonomic non-containing constraint is imposed on point 2, since its equation depends only on the coordinate and time. It is necessary to determine the number of the point on which the holonomic non-containing constraint is imposed. The answer to the problem is point 2.

By purchasing this digital product, you receive a complete and understandable solution to the problem, which will help you better understand this topic and successfully cope with further tasks. Solving a problem includes a description of the problem conditions, a step-by-step solution and an answer. The product is presented in HTML format, which allows you to conveniently view it on any device.

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Solution to problem 18.1.2 from the collection of Kepe O.?. consists in determining the number of the material point on which a holonomic non-containing constraint is imposed, based on the constraint equations imposed on each of the points.

Hopefully:

Material points 1 and 2 move in space.

Connection equation for point 1: x^2 + y^2 + z^2 - 25 = 0.

Connection equation for point 2: x^2 + y^2 + z^2 - 25t^2 ≤ 0.

We need to find the number of the point on which the holonomic non-restraining constraint is imposed.

Answer:

A holonomic relationship is a relationship that can be expressed as an equation between the coordinates of points and time. In this case, the connection equation for point 1 does not depend on time, but for point 2 it does.

The constraint equation for point 1 specifies a sphere of radius 5 centered at the origin. This means that point 1 is always located on this sphere and the connection holds it.

The constraint equation for point 2 also defines a sphere of radius 5 centered at the origin. However, since the equation is time dependent, the radius of the sphere will decrease with time. Point 2 can be located both on the sphere and inside it. If the point is on the sphere, then the connection to it is confining; if inside, then it is not confining.

Thus, a holonomic non-restraining constraint is imposed on point 2.

Answer: 2.

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