# Comparison of Tethered Post-Capture System Models for Space Debris Removal

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## Abstract

**:**

## 1. Introduction

## 2. Dynamic Models of the Tethered System

#### 2.1. Configuration of Tethered System

#### 2.2. Modified Dumbbell Model

#### 2.2.1. Single Tether Configuration

#### 2.2.2. Sub-Tether Configuration

#### 2.3. Lumped-Mass Model

#### 2.3.1. Single Tether Configuration

#### 2.3.2. Sub-Tether Configuration

#### 2.4. ANCF Model

#### 2.4.1. Single Tether Configuration

#### 2.4.2. Sub-Tether Configuration

## 3. Modal Analysis of Tethered System

#### 3.1. Analytical Results

#### 3.2. Modified Dumbbell Model

#### 3.3. Lumped-Mass Model

#### 3.4. ANCF Model

## 4. Comparison of Three Models

#### 4.1. Single Tether Configuration

#### 4.2. Sub-Tether Configuration

#### 4.3. Comparison of Natural Frequency

#### 4.4. Influence by Initial Condition

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Damage on Canadarm2 [2].

**Figure 3.**Configurations of a tethered system [27].

**Figure 16.**Convergence study of the lumped-mass model. (

**a**) Natural frequency convergence of the main tether; (

**b**) natural frequency convergence of the tethered system.

**Figure 17.**Convergence study of the ANCF model. (

**a**) Natural frequency convergence of the main tether; (

**b**) natural frequency convergence of the tethered system.

Parameter | Value | |
---|---|---|

Service Satellite | Mass ${m}_{S}$, (kg) | 10 |

Dimensions −, (m) | 0.6 × 0.6 × 0.6 | |

Target | Mass ${m}_{T}$, (kg) | 3.5 |

Dimensions −, (m) | 0.4 × 0.4 × 0.4 | |

Tether | Main tether length L, (m) | 2.25 |

Sub-tether length l, (m) | 0.4123 | |

Tether diameter d, (mm) | 5 | |

Damping coefficient c, (-) | 0.1 | |

Young’s modulus E, (Pa) | $4.456\times {10}^{7}$ |

Models | Screenshots of Animations |
---|---|

$\mathit{t}=0$ s $\mathit{t}=2.5$ s $\mathit{t}=5$ s | |

Modified Dumbbell Model | |

Lumped-mass Model | |

ANCF Model |

Models | Screenshots of Animations |
---|---|

$\mathit{t}=0$ s $\mathit{t}=2.5$ s $\mathit{t}=5$ s | |

Modified Dumbbell Model | |

Lumped-mass Model | |

ANCF Model |

Order | Analytical | Modified Dumbbell Model | Lumped-Mass Model | ANCF Model |
---|---|---|---|---|

1 | 71.59 | 45.58 | 71.24 | 71.59 |

2 | 143.19 | - | 142.46 | 143.19 |

3 | 214.78 | - | 213.65 | 214.79 |

4 | 286.38 | - | 284.79 | 286.44 |

5 | 357.97 | - | 355.86 | 358.22 |

Order | Analytical | Modified Dumbbell Model | Lumped-Mass Model | ANCF Model |
---|---|---|---|---|

1 | 1.947 | 1.949 | 1.948 | 1.948 |

2 | 71.646 | - | 74.574 | 71.647 |

3 | 143.216 | - | 147.555 | 143.217 |

4 | 214.802 | - | 217.549 | 214.814 |

5 | 286.392 | - | 283.120 | 286.464 |

Parameter | Value | |
---|---|---|

Service Satellite | Mass ${m}_{S}$, (kg) | 500 |

Dimensions −, (m) | 2.5 × 2.5 × 2.5 | |

Target | Mass ${m}_{T}$, (kg) | 8000 |

Dimensions −, (m) | 5 × 5 × 5 | |

Tether | Main tether length L, (m) | 100 |

Tether diameter d, (mm) | 50 | |

Damping coefficient c, (-) | 0.1 | |

Young’s modulus E, (GPa) | 131 |

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**MDPI and ACS Style**

Shan, M.; Shi, L.
Comparison of Tethered Post-Capture System Models for Space Debris Removal. *Aerospace* **2022**, *9*, 33.
https://doi.org/10.3390/aerospace9010033

**AMA Style**

Shan M, Shi L.
Comparison of Tethered Post-Capture System Models for Space Debris Removal. *Aerospace*. 2022; 9(1):33.
https://doi.org/10.3390/aerospace9010033

**Chicago/Turabian Style**

Shan, Minghe, and Lingling Shi.
2022. "Comparison of Tethered Post-Capture System Models for Space Debris Removal" *Aerospace* 9, no. 1: 33.
https://doi.org/10.3390/aerospace9010033