"His students meant the world to him -- indeed,
I cannot imagine my father as anything but a professor to generations of students.
From Linda Kane (Professor Kane's daughter).
With the death of Professor Kane, the world of Dynamics has lost its brightest star.
To dynamicists the world over, his method of formulating equations of the motion will remain as the best method to do dynamics.
Before the mid-sixties, the most-used method of predicting the motion of objects was due to the eighteenth century French scientist, Lagrange.
With the advent of the space age, a method was necessary that could treat the dynamics of complex systems with many moving parts, like a spacecraft, in a manageable way.
The method had to be the least laborious and yet be capable of producing the simplest possible equations.
That is where Kane's Equations fit the bill.
Kane, together with his students, not only produced computer solutions of equations describing the motions of complex systems, but also predicted the stability of such solutions.
Prof. Kane was a brilliant researcher, but his skills in teaching dynamics was equally brilliant.
He could not stand fuzzy thinking on the subject, and demanded precision in the definition of concepts.
His firm conviction was that one learns Dynamics by Doing, that is, by solving problems, and not by reading books or listening to lectures.
He also had his own sense of humor about these matters.
Prof. Kane was also a very kind human being.
In the face of great personal tragedy, he showed with his life how to live one's own.
I dedicated my flexible multibody dynamics books to him.
He inspired me in my work, wrote eight papers with me, and helped me find meaningful work.
Contributed by Dr. Arun Banerjee (Lockheed/Space systems Loral)
The inside front cover of my textbooks have:
"This book is dedicated to Thomas Kane who was
my dynamics instructor for five classes,
Stanford graduate dissertation advisor and teaching mentor for 15 quarters, and
professional colleague at Online Dynamics and Motion Genesis for 20+ years.
It has been one of my life's pleasures to discuss dynamics, current events,
and life events with Thomas Kane for thousands of hours over 30+ years."
Online Dynamics/Autolev company
By the time a group of students got to the third quarter of Dynamics,
they knew each other well enough to form a coed softball team.
Our team was made up of Professor Kane's students and their girlfriends/boyfriends/spouses.
Our team t-shirt was designed by a student who sat in Professor Kane's class.
He acted like he was taking notes but was actually drawing Professor Kane.
We weren't sure if Professor Kane would find the t-shirt (shown-right) amusing,
but he said he loved it.
Thank goodness for his wonderful sense of humor!
Contributed by Bev Sturgis (formerly Sandia National Labs)
Professor Kane trained generations of students.
Shown right is Professor Kane conversing with a young Keith Buffinton (now Bucknell professor).
The photo taken 30+ years thereafter shows Professor Kane with Jennifer Bower-Dawson,
who was trained at Bucknell by Keith Buffinton before her Ph.D. at Stanford.
In Jennifer's words:
"I am grateful for Professor Kane's generational influence and all of the ways he and his students have helped me to succeed."
Before her executive aerospace and autonomous-driving work,
Professor Bower-Dawson taught dynamics to yet another generation of college engineers.
Photo contributed by Professor Keith Buffinton (Bucknell)
"When life throws you a lemon, make some lemon aid. I prefer to make mine with some beer".
Professor Kane said this to me as he handed me a beer from his refrigerator
and we went to sit on his back deck to talk.
Tom told me when I discovered that part of what I was writing my PhD on was
going to appear in a paper Dan Rosenthal had submitted (and which Tom I believe had been asked to review).
Contributed by Professor Kurt Anderson (RPI)
It was in the 1960s, more than half a century ago, when each of us had the good fortune of attending his wonderful lectures,
marveling at his nurturing advice, absorbing his quick wits,
and becoming inspired that nonlinear mechanics was exciting, powerful, and ready to help launch our careers.
Professor Kane was not only a remarkable scholar in his own right,
but also a superb teacher-advisor in the sense that he made us learn with confidence and encouraged
each of us to gain more insight by teaching and demonstrating with examples.
In 2004, all of us got together and organized a symposium at Stanford celebrating
his 80th birthday with more than 40 of his former students in attendance.
At the symposium dinner, after many tributes of appreciation were said of him, Professor Kane responded with a smile,
"I thank you very much, and by the way, all you said was true." How delightful indeed !
Contributed by Wesley Brill, Jeffrey Fong, John Kaiser, Yas Kashiwagi, Dick Robe
Tom was, of course, a man of great intellectual ability,
but more importantly he was a good friend and a man of the highest integrity and standards.
He kept us on the straight and narrow in our faculty meetings,
occasionally having to remind us that we were proceeding in rather silly fashions.
Serving on a qualifying or University oral exam with him was always a rewarding and eye-opening experience,
as one could watch the quality interactions with students for which he was famous.
Tom always sought precise and rational thinking, in both himself and others.
Not only will he be missed as a colleague and friend,
but his adherence to and appreciation of sound thinking will be missed in our future academic landscape.
Contributed by Professor Emeritus David Barnett (Stanford University)
Anyone fortunate enough to have taken courses from Professor Kane,
or who has studied dynamics using any of his excellent books,
will recognize and appreciate material presented with exceptional clarity, precision, and utility.
Clear precise definitions, impeccable derivations, and judicious ordering of topics
set Professor Kane's work apart from all the rest.
As an example where a familiar concept is put on a more solid foundation, consider angular velocity.
With the aid of a suitable definition, certain important theorems can be readily and rigorously
proven compared to the fuzzy hand-waving explanations typically found elsewhere.
Contributed by Dan Weber
I read that the highest purpose a life can achieve is to attempt great things,
experience great failures and great successes, and from them gain wisdom.
And then in your time pass them on to those after you.
Professor Kane turned that schedule upside down,
had his successes starting early in life
and spent the majority of his time
passing his hard fought wisdom onto thousands of students.
He took the confusing cluttered world of dynamics and forged a clear path through it.
He had enormous respect for his students and their hard work of learning.
He generously taught them with care to make sure we got
everything we needed to understand the topic, and nothing more.
His goal was to make sure we understood as easily as possible,
led us along pointing out the paths and the ways around the obstacles.
And then he stepped back at the end and we found ourselves on the top of a mountain
we never dared thought we could ever climb.
He took this "C" student and turned him into an "A+",
something no other professor had accomplished before or since.
And left him with a love of his topic.
Contributed by Albert Hartman
Professor Kane was my favorite instructor from my graduate student days at Stanford. He took a
subject that I thought I would never understand and made it understandable - so much so that I now
teach it at a university. He was the clearest lecturer I ever had, and his precise way of
explaining difficult concepts has had a huge positive influence on the way I teach my engineering
I knew I would like being in Prof. Kane's courses from the very first lecture. As he was
explaining his expectations for the course, he shared a comment that made me chuckle. He said that
he did not like it when students brought food or drinks to lecture, since he had had students
spill their food and drinks and disrupt his lectures. Then he shared his famous quote, "I won't
lecture in your dining hall if you don't eat in my lecture room." Seemed like a fair agreement to
Prof. Kane had a very graphic way of teaching. He was constantly trying to help his students
visualize the concepts he was seeking to convey. It was not unusual for him to make a comment
like, "You could paint a green dot on it," to help students understand some aspect of a physical
Prof. Kane was also on my PhD dissertation committee, and I visited him frequently to get input on
how to develop the model and derive the dynamics equations for my project. Prof. Kane was always
happy to meet with me whenever I had questions. We often met in his office, but as I started
ramping up on my PhD dissertation project, he began inviting me over to his home to teach me about
a new computer program that he thought could help me with my dissertation - Autolev. He was
extremely excited about the possibilities that Autolev opened up by eliminating tedious and
error-prone symbol manipulation, and he wanted to share his discovery with anyone who might
benefit from it. I certainly benefitted - and have continued to benefit - from that initial
introduction. I could not have completed my dissertation project without the help of Autolev, and
I continue to use Autolev's successor to this day for teaching dynamics and deriving dynamics
equations for various research projects.
One of my favorite memories of Prof. Kane is his sense of humor. I am good friends with one of
Prof. Kane's former Ph.D. students - Greg Woodward. I was best man in Greg's wedding, and so I had
the honor of organizing a bachelor party for Greg. We decided to blindfold Greg and take him to
different places where we would take Polaroid photos of him doing something embarrassing. One of
the stops was Prof. Kane's house. We had Greg sit on the sofa in the living room and then guess
where he was. Prof. Kane was sitting on the sofa right next to him, and we took a picture of the
two of them sitting next to each other - Prof. Kane with a huge smile on his face, and Greg
blindfolded. Then we asked Greg to guess where he was. Greg sniffed in the air a few times,
grasped a sofa cushion with his hand, and then said, "It smells really musty in here, and this
sofa feels really cheap. Must be some old person's house." It was all we could do not to burst out
laughing, and Prof. Kane didn't bat an eye. His smile only grew larger, realizing how embarrassed
Greg would be when we showed him the Polaroid photo later.
At my dissertation defense, Prof. Kane had another great sense-of-humor moment. I had worked hard
on writing my dissertation - it was close to 200 pages long, and needless to say it was rather
wordy. At the end of my defense, my dissertation advisor, Prof. Felix Zajac, asked the committee
members if they had any comments on the written document. Prof. Kane was the first to respond,
sharing the following comment: "This dissertation is extremely well written. In fact, you could
take out ever other page and it would still be extremely well written." That was about the nicest
way someone could say that my dissertation was extremely wordy and needed to be tightened up a lot
before final submission.
I eventually moved out of the Bay Area to start my first faculty position in Florida. In my early
days as new faculty member, I would e-mail Prof. Kane periodically with questions about teaching
dynamics. I always received a prompt, thorough, and extremely helpful response that resolved my
question and gave me new insight into how to teach some aspect of dynamics. Long after I graduated
from Stanford, Prof. Kane was still willing to share his teaching abilities with me to help me
become a better teacher myself.
After my move to Florida, I had to visit Stanford periodically for work-related trips, and
whenever I had some extra time, I would try to stop by to visit Prof. Kane. As his health
deteriorated gradually, what amazed me was the positive attitude that he always maintained, along
with the learning spirit that he always exhibited. I remember my first visit to the retirement
home where he and Mrs. Kane had moved, across from the Stanford med school. We had lunch together,
and then Prof. Kane invited me up to his apartment to show me his setup for reading from a large
computer screen. At some point, we started talking about what he could still see. He had a piece
of crumpled up cellophane next to his computer, and he told me to go over to the window, look out
toward the foothills, and put the piece of crumpled cellophane over my eyes. That is what he could
still see. He didn't share the analogy out of anger or frustration but out of a desire to teach me
about what he was experiencing. He was always teaching, regardless of what he was doing.
On a later visit after he had completely lost his sight, I walked into the foyer of the retirement
home and heard someone playing a beautiful song on the piano. As I walked closer to the piano, I
soon realized it was Prof. Kane who was playing. After I greeted him, I informed him that I didn't
realize he played the piano. Without thinking, he replied, "Well, now that I'm blind, I thought I
would take up the piano. That's what blind guys do." Again, he made the comment not out of anger
or frustration but out of a desire to make the best of a difficult situation. He was very proud of
his piano playing and even sent a recorded song to me via e-mail after I left.
One of the main reasons I wanted to become a professor was to make a positive impact on the lives
of the students I teach. That is what Prof. Kane did for me - left a positive impact that has made
me a much better professor than I would have been otherwise. I will greatly miss his whit and
humor, his unswerving positive attitude, and his desire to help his students become the best
people they can be.
Contributed by Professor B.J. Fregly (Rice University)
Professor Kane was very dedicated to his family, his students and his friends.
His wit, kindness, ethics and personal philosophy were present in almost everything he said and did.
Although I missed Professor Kane's dynamics courses during my masters at Stanford in 1980,
I met with him several times for advice on a designing Handbike (a student design project for an arm-powered bike).
This was the beginning of a long friendship.
As a springboard diver and coach, I often saw Professor Kane at the Stanford pool where he swam at lunch time.
He took time to show me how a cat turns to land on its feet,
and gave me instructions on how I might replicate the trick from the diving board, or while submerged in the water.
I worked with Professor Kane to prototype a unicycle with a weight below its axle to investigate stability.
We pushed it across an empty parking lot and it seemed the weight helped keep it rolling for a greater distance.
These and other adventures/projects were typically followed by a delightful dinner with Professor Kane and Ann.
Our histories crossed shared adventures on time-lines 30 years apart.
We both studied at Columbia (we even had the same professor, Dudley Fuller);
visited Novosibirsk Siberia
(Professor Kane as a visiting lecturer, I as a tourist); visited Nepal, ...
I looked forward to visiting Professor Kane and Ann at the Palo Alto Hyatt/Vi retirement community
were we discussed his latest inventions such as "HangUps", which was a red string with alligator clips
that could conveniently suspended everything from most any connection point (e.g., a shirt collar, wall, or suspenders).
Even when he was struggling with his loss of sight and hearing,
he was always strong, dignified and more concerned with others around him than his own challenges.
He was always the professor, someone I could turn to for stimulating conversation,
advice and friendship ... and that lives on in vivid memories.
Contributed by Doug Schwandt (Stanford diving coach/Schwandt Mechanical Design)
TR Kane with students/now Professors
TR Daniel Jacobs (Temple) and Michael Zabala (Auburn)
While I never met Professor Kane,
I became a dedicated practioner of Kane's Method in 1988, first by hand, then through Autolev, and currently through Motion Genesis.
I was trained by Bob Ryan (a first-generation Kane disciple) who later co-advised my Ph.D. thesis.
In addition to Bob Ryan, I have been fortunate to interact with other Dr. Kane first-generation disciples: Dewey Hodges, Keith Buffington, Arun Banerjee, and Paul Mitiguy, and have the upmost respect for them all.
Unfortunately, I believe that Dr. Kane's contribution to the advancement of theoretical dynamics is not yet fully appreciated for its significance.
By developing Kane's method, Dr. Kane is in an orbit near Newton, D'Alembert, and Lagrange.
Dr. Kane's emigration from Europe in the dark days prior to WWII, his later military service during WWII,
and his presence on the USS Missouri when the Japanese surrendered places him squarely in the greatest generation
(he exemplifies why they are called the greatest generation).
He later joined the earlier great scientific minds from Europe to America who had helped the US win WWII
and drove US scientific advancement to the forefront of the World.
His death leaves the Dynamics world diminished.
However his contributions and those of his students to the advancement of the field of dynamics live on.
May he rest in peace and enjoy eternal satisfaction.
Contributed by Bill Haering (Sandia National Labs)
Kane's school of dynamics.
Professor Kane contended that the only legitimate purpose for dynamics was to use it to solve physically meaningful problems.
His philosophy of dynamics was that it is a subject dealing entirely with details – omit the details and nothing remains.
His uncompromising belief that precision of expression and clarity of thought affect each other profoundly compelled him to
leave no topic in kinematics or dynamics to the mercy of adherents of other philosophies of dynamics,
insisting on operational definitions of every quantity he worked with.
Professor Kane's crowning achievement was the development of a new way to formulate equations of motion for any
system of rigid bodies and particles, one that requires a minimal amount of labor,
leads to equations having the simplest form, and is the easiest method to teach and to learn.
Contributed by David Levinson (Lockheed/Space Systems Loral/Maxar Space Infrastructure)