## 3 Results  
### Energy Transformation of Tsukahara and Yurchenko Vaults  
Upon springboard contact, considering all Tsukahara vaults, TKE comprised 72% of total energy on average (Figure 4). During board contact, both total energy (\(-\)2%) and TKE (\(-\)26%) diminished whereas, AKE (+70%) and PE (+23%) increased. During table contact, total energy (\(-\)6%), TKE (\(-\)58%), and AKE (\(-\)6%) decreased, but PE increased (+38%). After push-off from the vault (during the second flight phase), total energy continued to increase by 9%, achieving a maximal value during the second flight phase within 1% of that at the initial springboard contact. This increase in total energy corresponded with 33% and 13% increases in AKE and PE, respectively.  
Upon springboard contact, considering all Yurchenko vaults, average total energy consisted of 49% TKE, 27% PE, and 25% AKE (Figure 5). During the springboard contact phase, total energy and PE increased by 8% and 29%, respectively, whereas TKE (\(-\)0.3%) and AKE (\(-\)4%) remained similar. During the table contact phase, total energy (\(-\)7%), TKE (\(-\)46%), and AKE (\(-\)30%) diminished, whereas PE increased by 27%. During the second flight phase, total energy increased by 9%, attaining a maximal value 10% higher than that at initial springboard contact. Further, AKE and PE during the second flight phase were 31% and 15% higher, respectively, than at push off from the table.  
Comparison of Yurchenko and Tsukahara vaults revealed that total energy at initial springboard contact is 7% lower for Yurchenko vaults than for Tsukahara vaults on average (\(p=0.16\), r = 0.48). However, total energy levels in all other phases of the vault were higher for Yurchenko vaults (mean differences of 4-5%; \(p\): from 0.12 (landing) to 0.005 (table on)); r: from 0.37 (landing) to 0.52 (table on)). Additionally, we found higher TKE during springboard contact and the first flight phase (+15% to +37%; \(p\): from 0.001 (board on) to 0.0001 (board off and table on); r: from 0.67 (table on) to 0.85 (board on)) but lower PE (\(-\)3% to \(-\)17%; \(p\): from 0.25 (board on) to 0.0001 (table on); r: from 0.41 (board on)) and AKE (\(-\)6% to \(-\)82%; \(p\): from 0.87 (landing) to 0.0001 (board off and table on)); r: from 0.02 (landing) to 0.0001 (board off and table on)) during all phases for Tsukahara vaults compared to Yurchenko vaults.  
Figure 4: Averaged flux of different energy forms across the different vault phases of simple and difficult Tsukahara vaults (Tsukahara layout without (n = 5) and with 360\({}^{\circ}\) (n = 11), 720\({}^{\circ}\) (n = 10), and 900\({}^{\circ}\) (n = 2) of rotation around longitudinal axis during second flight phase). TKE: translational kinetic energy; PE: potential energy; and AKE: angular kinetic energy.  
Figure 5: Averaged flux of different energy forms across the different vault phases of simple and difficult Yurchenko vaults (Yurchenko layout without layout (n = 5) and with 360\({}^{\circ}\) (n = 4), 720\({}^{\circ}\) (n = 7), and 900\({}^{\circ}\) (n = 4) of rotation around longitudinal axis during second flight phase). TKE: translational kinetic energy; PE: potential energy; and AKE: angular kinetic energy.