Common Forces in Mechanics
Of the forces commonly encountered when solving problems in Newtonian mechanics, introductory texts usually limit illustrations of the definitions of conservative and non-conservative forces to gravity, spring forces, kinetic friction and fluid resistance. However, at the expense of very little class time, the question of whether each of the common forces is conservative or non-conservative can be settled once and for all. I provide here brief arguments for classroom use that establish the conservative or non-conservative nature of each force commonly encountered in mechanics problems, including forces whose conservative or non-conservative natures are seldom or never addressed by textbooks.
This book covers new theoretical and numerical developments in the mechanics of material forces. Conceptually speaking, common continuum mechanics in the sense of Newton – which gives rise to the notion of spatial (mechanical) forces – considers the response to variations of spatial placements of "physical particles” with respect to the ambient space, whereas continuum mechanics in the sense of Eshelby – which gives rise to the notion of material forces – is concerned with the response to variations of material placements of "physical particles” with respect to the ambient material. Well-known examples of material forces are driving forces on defects like the Peach-Koehler force, the J-Integral in fracture mechanics, and energy release. The consideration of material forces goes back to the works of Eshelby, who investigated forces on defects; therefore this area of continuum mechanics is sometimes denoted Eshelbian mechanics.
There are common features of high velocity throwers that you will not see in most high school or college pitchers...certainly not Little League pitchers.
Here is video comparison of Royal's Zach Greinke and Red Sox Daniel Bard that shows features that are similar in both pitchers. Notice how their timing is almost exact as they move from the back leg to the front leg and then into ball release. Timing of the parts is a key ingredient that insures that forces are efficiently transferred from the body to the arm...so there is less stress on the arm.
The common features you will observe here that you will not see in most high school, college or Little League pitchers are: 1. Early weight shift - get the hip going out first
2. Do not rotate early over the back leg
3. Have explosive leg drive
4. Complete leg drive before landing
5. Land with the trunk and the throwing arm and shoulder still back so the arm gets involved late
6. Bracing action of the hip, knee and ankle upon landing to speed up the trunk and the arm.
Students can also get help on A Brief Introduction to Fluid Mechanics involving different topics from the online tutors.
These are the mechanical skills that all pitchers should be working on to improve during the off-season. When we one-on-one lessons here at our facility in Scottsdale, AZ these are the mechanical adjustments we help pitchers make whether they are high school, college or professional pitchers.
It is quite clear that these common features of high velocity throwers have little to do with arm strength since the arm gets involved very late in the delivery. In fact, sports science research has proven that arm strength has little to do with pitching velocity. Thus why long toss or weighted balls or weight training will not improve pitching velocity.
It is the speed of rotation of the trunk that whips the pitcher's arm through. Trunk rotation speed is all about the forward momentum of the body going from the back leg to the front leg and then finally the bracing action of the front leg and hip.