## 1 Introduction  
The start of the New Space paradigm has changed the development philosophy of the worldwide space-engineering field. New Space refers to the recent commercialization of the space sector, which is mainly led by private industries, rather than government-funded organizations. These industries are driving a better, faster, cheaper, and lighter space-development paradigm [1, 2, 3, 4]. One of the major accelerators of the New Space paradigm is the emergence of small satellite constellations. The large-volume production of small satellites, based on a standardized satellite platform and commercially available on-board hardware, has reduced the development cost and schedule. In addition, the total launch cost can be reduced as multiple small satellites are launched together. These advantages make the small-satellite platform attractive for various challenging missions that require high temporal system performance, e.g., real-time remote sensing, global internet services, and high-speed communications [4]. All satellites undergo various dynamic loads during the launch phase. These loads involve steady-state acceleration caused by the engine thrust, sinusoidal vibration caused by the engine cutoff, and a self-excited vibration, called the pogo effect, from the combustion instability of the launcher. Random vibrations are caused by the noise of the thrust, and mechanical shock is induced by the separation of the launcher stages and spacecraft. Because these dynamic loads are extremely severe and complex, they are one of the major factors that cause satellites and components to malfunction [5]. Therefore, a proper structural design is essential to ensure the structural safety of the satellite in the launch environment. Two approaches are used to enhance the structural safety of satellites during the design phase. One traditional approach is to design the spacecraft structure such that it has sufficient strength and stiffness to endure mechanical loading. However, this approach faces the technical issue on limitation in minimizing the mass and volume of the satellite, especially in small satellites with design limitations of their volume and mass. These factors are related to the available number of satellites that can be launched within the lift capability of the launcher and, therefore, directly lead to an increase in launch costs. The other method involves reducing the launch loads transmitted to the satellite by applying a whole-spacecraft vibration isolator (WSVI). The WSVI is achieved by implementing a low-stiffness and high-damping capability, compared to the conventional concept, which is rigidly mounted between the satellite and launch adaptor. This makes it possible to effectively reduce the mass and volume of the satellite by minimizing the design load of vibration-sensitive components. In addition, it can contribute to reducing the satellite's development cost and schedule by optimizing the conventional verification process, which accounts for a large portion of the time and cost of satellite-development programs. In addition, the on-ground test process can be optimized, e.g., simplifying and skipping the test phases of the subsystem-level verification. For example, verification can be performed at a higher system level of the integrated test because using the WSVI greatly reduces the potential technical risks to the vibration-sensitive components at the subsystem level. Another possible test schedule mitigation might also be expected on the notching process in the launch-vibration tests because creating a proper notched input level takes a large portion of the time. These potential advantages of WSVIs are attractive for the New Space based development trend to achieve the goal of cost-effective small satellite development. Several previous studies have been conducted to realize whole-spacecraft vibration isolators. [PERSON] et al. [6] proposed WSVI systems called SoftRide UniFlex and SoftRide MultiFlex to realize launch-vibration isolation for the MINOTAUR/JAWSAT program.