# Scleronomic constraint with explicit time dependence?

• kokolovehuh
In summary, the conversation discusses the term scleronomic constraint and its relation to time dependence in a holonomic system. It is mentioned that scleronomic constraints are independent of time, but there is still time dependence in the generic dynamic variable q. The speaker is confused about whether there can be explicit time dependence in scleronomic constraints, as they have read conflicting information.
kokolovehuh
Hi all,
I was having a bit difficulty understanding the term scleronomic constraint.
From what I have read, it is a type of holonomic system(which means there is time dependence). However, the difference between the two types(scleronomic and rheonomic), is that although scleronomic constraint is independent of time there is still time dependence in q(generic dynamic variable). This leads me to think that there is an explicit time dependence in that type of constraint. Yet, from what I read from a book, it says scleronomic constraint cannot have explicit time dependence. How is this the case?

Regards

Owen

correction: the time dependence refers to the Lagrangian, which are under the scleronomic constrain in this case.

## 1. What is a scleronomic constraint with explicit time dependence?

A scleronomic constraint with explicit time dependence is a type of constraint in which the motion of a system is restricted based on the positions of its components at a specific time. This means that the constraint is not only dependent on the positions of the components, but also on the specific time at which those positions are measured.

## 2. How is a scleronomic constraint with explicit time dependence different from other types of constraints?

A scleronomic constraint with explicit time dependence differs from other types of constraints, such as holonomic or non-holonomic constraints, in that it explicitly includes the element of time in its definition. This means that the constraint cannot be fully described without taking time into account.

## 3. What are some examples of systems that exhibit scleronomic constraints with explicit time dependence?

One example is a pendulum, where the length of the string is a scleronomic constraint that is dependent on time as the pendulum swings back and forth. Another example is a rotating rigid body, where the angular velocity is a scleronomic constraint that is dependent on time.

## 4. How do scleronomic constraints with explicit time dependence affect the dynamics of a system?

Scleronomic constraints with explicit time dependence can significantly impact the dynamics of a system by imposing additional restrictions on its motion. This can lead to more complex and difficult equations of motion, as well as unique behaviors and phenomena.

## 5. What are some applications of scleronomic constraints with explicit time dependence in scientific research?

Scleronomic constraints with explicit time dependence have various applications in fields such as mechanics, robotics, and astrophysics. They are often used to model and analyze complex systems, as well as to understand the effects of time on the dynamics of these systems.

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