# Is this system symetric enough? - classical dynamics

• Choi hoseung
In summary, designing a satellite system with daughter satellites orbiting in formation in three orthogonal planes to measure flyby anomaly effects may require numerical methods to calculate non-linear effects and predict kinetic energy fluctuations. The specifics will depend on the chosen model.
Choi hoseung
I'm designing a satellite( flying in formation).
It looks like 3 couples of daughter-satellites(180degree apart) orbiting around the mother satellite in 3 orthogonal planes to measure flyby anomally effect. I want to measure the effect in 3-separate directions. But I'm afraid that the orbiting pairs would effect each others in non-linear way. Will the other two couples the ohter? then at least is it possible to calibrate that effect in systematic calculation? or is the effect only able to be computed numerically? - I need it to be solvable in analytic way.

to make it celarer, let's say:
at time = 0;
mother is at the origin(0,0) - Center of Mass
daughter-x1 at (-1,0,0) x2 (1,0,0)
y1 (0.2.0) y2(0.-2.0)
z1(0.0.3) z2(0.0-3) (distinct separations to avoid collision)
then, they start to orbit in independent periods.

- one more, if this system it self orbit around the earth, is the fluctuation(due to varying configuration of its daughters) of mother's kinetic energy predictable? how about individual daughters kinetic energy?

Last edited:
The answer to your questions depends on the specific model you are using. It is possible to calculate the non-linear effects of the orbiting pairs on each other, but it would likely require numerical methods as opposed to analytical. If the system is orbiting around the Earth, then the fluctuation of the mother's kinetic energy can be predicted, but again this will depend on the specific model you are using. The same applies to the individual daughters' kinetic energies.

## 1. What does it mean for a system to be symmetrical in classical dynamics?

In classical dynamics, a system is considered symmetrical if it remains unchanged under certain transformations, such as rotations, reflections, or translations. This symmetry allows for the conservation of important physical quantities, such as energy and momentum.

## 2. How do you determine if a system is symmetrical enough?

Determining if a system is symmetrical enough is based on the level of symmetry present in the system. This can be determined through mathematical calculations and analysis, as well as experimental observations and measurements.

## 3. Can a system be too symmetrical in classical dynamics?

It is possible for a system to be too symmetrical in classical dynamics, which can lead to complications and difficulties in understanding its behavior. An overly symmetrical system may also limit its range of possible outcomes and hinder its ability to adapt to changing conditions.

## 4. What are some examples of symmetrical systems in classical dynamics?

Some common examples of symmetrical systems in classical dynamics include a pendulum, a swinging spring, a spinning top, and a simple harmonic oscillator. These systems exhibit symmetrical behavior and are often used to model more complex systems.

## 5. How does symmetry play a role in classical dynamics?

Symmetry is a fundamental concept in classical dynamics and plays a crucial role in determining the behavior and properties of physical systems. It allows for the prediction and understanding of various physical phenomena and is an essential tool in the study of classical dynamics.

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